Abstract group data - 2880.hl

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [3, 3, 6, 12, 2, 2, 2, 6, 60], 'aut_gens': [[11, 840, 3670571, 8025137, 7, 5, 23, 124, 50804050], [11, 840, 3670571, 8025130, 23, 6, 16, 128, 50804049], [11, 840, 3670571, 8025137, 7, 5, 23, 1564, 50804050], [11, 840, 164063531, 123420970, 23, 6, 16, 728, 80237649], [8, 840, 131364008, 160031529, 16, 6, 23, 731, 127774930], [20, 840, 3670580, 8025142, 7, 14, 23, 128, 50804050], [19, 840, 3670579, 8025133, 23, 5, 7, 123, 50804062], [12, 840, 3670572, 8025137, 7, 14, 23, 135, 50804053], [12, 1440, 3669972, 8024538, 16, 2, 7, 124, 50804657], [4, 840, 131364004, 160031537, 7, 2, 16, 1572, 50804058]], 'aut_group': '2880.hl', 'aut_hash': 799193401477229059, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2880, 'aut_permdeg': 14, 'aut_perms': [164133512, 4354969080, 4069535740, 4094543449, 123747120, 124108712, 126288152, 84838496, 86180832618], 'aut_phi_ratio': 3.75, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 2], [2, 5, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 15, 1, 2], [2, 18, 1, 1], [2, 30, 1, 1], [2, 45, 1, 1], [2, 90, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 5, 1, 2], [4, 6, 1, 1], [4, 15, 1, 4], [4, 18, 1, 1], [4, 30, 1, 5], [4, 45, 1, 2], [4, 90, 1, 5], [5, 4, 1, 1], [6, 6, 1, 1], [6, 10, 1, 1], [6, 12, 1, 1], [6, 24, 1, 1], [6, 30, 1, 1], [6, 40, 1, 1], [6, 60, 1, 1], [6, 80, 1, 1], [6, 120, 1, 1], [10, 12, 1, 2], [10, 24, 1, 1], [10, 36, 1, 1], [10, 72, 1, 1], [12, 10, 1, 2], [12, 12, 1, 1], [12, 30, 1, 2], [12, 40, 1, 2], [12, 60, 1, 5], [12, 80, 1, 2], [12, 120, 1, 2], [15, 8, 1, 1], [15, 32, 1, 1], [15, 64, 1, 1], [20, 24, 1, 1], [20, 72, 1, 1], [30, 24, 1, 1], [30, 48, 1, 1], [30, 96, 1, 1], [60, 48, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times F_5\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '2880.hl', 'autcentquo_hash': 799193401477229059, 'autcentquo_nilpotent': False, 'autcentquo_order': 2880, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times F_5\\times S_4', 'cc_stats': [[1, 1, 1], [2, 3, 2], [2, 5, 1], [2, 6, 1], [2, 9, 1], [2, 15, 2], [2, 18, 1], [2, 30, 1], [2, 45, 1], [2, 90, 1], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 5, 2], [4, 6, 1], [4, 15, 4], [4, 18, 1], [4, 30, 5], [4, 45, 2], [4, 90, 5], [5, 4, 1], [6, 6, 1], [6, 10, 1], [6, 12, 1], [6, 24, 1], [6, 30, 1], [6, 40, 1], [6, 60, 1], [6, 80, 1], [6, 120, 1], [10, 12, 2], [10, 24, 1], [10, 36, 1], [10, 72, 1], [12, 10, 2], [12, 12, 1], [12, 30, 2], [12, 40, 2], [12, 60, 5], [12, 80, 2], [12, 120, 2], [15, 8, 1], [15, 32, 1], [15, 64, 1], [20, 24, 1], [20, 72, 1], [30, 24, 1], [30, 48, 1], [30, 96, 1], [60, 48, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '2880.hl', 'commutator_count': 1, 'commutator_label': '180.31', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '5.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 194, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['20.3', 1], ['24.12', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 2], [2, 5, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 15, 1, 2], [2, 18, 1, 1], [2, 30, 1, 1], [2, 45, 1, 1], [2, 90, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 5, 2, 1], [4, 6, 1, 1], [4, 15, 2, 2], [4, 18, 1, 1], [4, 30, 1, 1], [4, 30, 2, 2], [4, 45, 2, 1], [4, 90, 1, 1], [4, 90, 2, 2], [5, 4, 1, 1], [6, 6, 1, 1], [6, 10, 1, 1], [6, 12, 1, 1], [6, 24, 1, 1], [6, 30, 1, 1], [6, 40, 1, 1], [6, 60, 1, 1], [6, 80, 1, 1], [6, 120, 1, 1], [10, 12, 1, 2], [10, 24, 1, 1], [10, 36, 1, 1], [10, 72, 1, 1], [12, 10, 2, 1], [12, 12, 1, 1], [12, 30, 2, 1], [12, 40, 2, 1], [12, 60, 1, 1], [12, 60, 2, 2], [12, 80, 2, 1], [12, 120, 2, 1], [15, 8, 1, 1], [15, 32, 1, 1], [15, 64, 1, 1], [20, 24, 1, 1], [20, 72, 1, 1], [30, 24, 1, 1], [30, 48, 1, 1], [30, 96, 1, 1], [60, 48, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1935360, 'exponent': 60, 'exponents_of_order': [6, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[24, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2880.hl', 'hash': 799193401477229059, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [3, 3, 6, 12, 2, 2, 2, 6, 60], 'inner_gens': [[11, 840, 3670571, 8025129, 16, 21, 7, 135, 50804057], [11, 840, 3670571, 8025137, 7, 5, 23, 1564, 50804050], [11, 840, 3670571, 8025129, 16, 21, 7, 735, 80237657], [15, 840, 3670575, 8025137, 7, 21, 16, 731, 127774929], [12, 840, 3670572, 8025137, 7, 14, 23, 135, 50804053], [19, 840, 3670579, 8025133, 23, 5, 7, 123, 50804062], [20, 840, 3670580, 8025142, 7, 14, 23, 128, 50804050], [20, 1440, 3669980, 8024530, 23, 1, 16, 124, 50804658], [4, 840, 164063524, 123420978, 16, 1, 23, 1580, 50804050]], 'inner_hash': 799193401477229059, 'inner_nilpotent': False, 'inner_order': 2880, 'inner_split': True, 'inner_tex': 'S_3\\times F_5\\times S_4', 'inner_used': [1, 2, 3, 4, 6, 8, 9], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 16], [2, 16], [3, 16], [4, 8], [6, 8], [8, 4], [12, 4], [16, 1], [24, 2]], 'label': '2880.hl', 'linC_count': 512, 'linC_degree': 9, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 128, 'linQ_dim': 9, 'linQ_dim_count': 128, 'linR_count': 128, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'S3*F5*S4', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 75, 'number_characteristic_subgroups': 70, 'number_conjugacy_classes': 75, 'number_divisions': 60, 'number_normal_subgroups': 70, 'number_subgroup_autclasses': 964, 'number_subgroup_classes': 964, 'number_subgroups': 15912, 'old_label': None, 'order': 2880, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 239], [3, 26], [4, 784], [5, 4], [6, 382], [10, 156], [12, 872], [15, 104], [20, 96], [30, 168], [60, 48]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 8], [4, 10], [6, 8], [8, 5], [12, 6], [16, 1], [24, 2]], 'representations': {'PC': {'code': '21522185185716292696711620568826601672798636284756590689059687996771809905710317640448294086764609405212', 'gens': [1, 2, 3, 6, 9], 'pres': [9, 2, 2, 2, 2, 3, 2, 3, 5, 2, 26245, 39422, 6761, 74, 79203, 732, 102, 66244, 733, 72590, 20759, 15908, 7493, 158, 33279, 3048, 3057, 249, 10393, 10402, 174968, 29177, 43766, 7325, 10979]}, 'Perm': {'d': 12, 'gens': [11, 840, 3670571, 8025137, 7, 5, 23, 124, 50804050]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times F_5\\times S_4', 'transitive_degree': 60, '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: 157604317
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 194, 'group_order': 2880, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 157604328
    {'aut_label': '2A', 'centralizer': '3.b1.a1', 'counter': 2, 'group_counter': 194, 'group_order': 2880, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 16, 'size': 3}
  • id: 157604339
    {'aut_label': '2B', 'centralizer': '3.a1.a1', 'counter': 3, 'group_counter': 194, 'group_order': 2880, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 1560, 'size': 3}
  • id: 157604350
    {'aut_label': '2C', 'centralizer': '5.a1.a1', 'counter': 4, 'group_counter': 194, 'group_order': 2880, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 3669120, 'size': 5}
  • id: 157604361
    {'aut_label': '2D', 'centralizer': '6.c1.a1', 'counter': 5, 'group_counter': 194, 'group_order': 2880, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 1, 'size': 6}
  • id: 157604372
    {'aut_label': '2E', 'centralizer': '9.a1.a1', 'counter': 6, 'group_counter': 194, 'group_order': 2880, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 127, 'size': 9}
  • id: 157604383
    {'aut_label': '2F', 'centralizer': '15.a1.a1', 'counter': 7, 'group_counter': 194, 'group_order': 2880, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 87091320, 'size': 15}
  • id: 157604390
    {'aut_label': '2G', 'centralizer': '15.b1.a1', 'counter': 8, 'group_counter': 194, 'group_order': 2880, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 3669127, 'size': 15}
  • id: 157604391
    {'aut_label': '2H', 'centralizer': '18.a1.a1', 'counter': 9, 'group_counter': 194, 'group_order': 2880, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 721, 'size': 18}
  • id: 157604318
    {'aut_label': '2I', 'centralizer': '30.a1.a1', 'counter': 10, 'group_counter': 194, 'group_order': 2880, 'label': '2I', 'order': 2, 'powers': [1, 10, 10], 'representative': 87091202, 'size': 30}
  • id: 157604319
    {'aut_label': '2J', 'centralizer': '45.a1.a1', 'counter': 11, 'group_counter': 194, 'group_order': 2880, 'label': '2J', 'order': 2, 'powers': [1, 11, 11], 'representative': 3669247, 'size': 45}
  • id: 157604320
    {'aut_label': '2K', 'centralizer': '90.a1.a1', 'counter': 12, 'group_counter': 194, 'group_order': 2880, 'label': '2K', 'order': 2, 'powers': [1, 12, 12], 'representative': 3669845, 'size': 90}
  • id: 157604321
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 13, 'group_counter': 194, 'group_order': 2880, 'label': '3A', 'order': 3, 'powers': [13, 1, 13], 'representative': 840, 'size': 2}
  • id: 157604322
    {'aut_label': '3B', 'centralizer': '8.i1.a1', 'counter': 14, 'group_counter': 194, 'group_order': 2880, 'label': '3B', 'order': 3, 'powers': [14, 1, 14], 'representative': 3, 'size': 8}
  • id: 157604323
    {'aut_label': '3C', 'centralizer': '16.g1.a1', 'counter': 15, 'group_counter': 194, 'group_order': 2880, 'label': '3C', 'order': 3, 'powers': [15, 1, 15], 'representative': 1455, 'size': 16}
  • id: 157604324
    {'aut_label': '4A1', 'centralizer': '5.a1.a1', 'counter': 16, 'group_counter': 194, 'group_order': 2880, 'label': '4A1', 'order': 4, 'powers': [4, 17, 16], 'representative': 11612160, 'size': 5}
  • id: 157604325
    {'aut_label': '4A-1', 'centralizer': '5.a1.a1', 'counter': 17, 'group_counter': 194, 'group_order': 2880, 'label': '4A-1', 'order': 4, 'powers': [4, 16, 17], 'representative': 8023680, 'size': 5}
  • id: 157604326
    {'aut_label': '4B', 'centralizer': '6.e1.a1', 'counter': 18, 'group_counter': 194, 'group_order': 2880, 'label': '4B', 'order': 4, 'powers': [2, 18, 18], 'representative': 18, 'size': 6}
  • id: 157604327
    {'aut_label': '4C1', 'centralizer': '15.b1.a1', 'counter': 19, 'group_counter': 194, 'group_order': 2880, 'label': '4C1', 'order': 4, 'powers': [4, 20, 19], 'representative': 11612167, 'size': 15}
  • id: 157604329
    {'aut_label': '4C-1', 'centralizer': '15.b1.a1', 'counter': 20, 'group_counter': 194, 'group_order': 2880, 'label': '4C-1', 'order': 4, 'powers': [4, 19, 20], 'representative': 8023687, 'size': 15}
  • id: 157604330
    {'aut_label': '4D1', 'centralizer': '15.a1.a1', 'counter': 21, 'group_counter': 194, 'group_order': 2880, 'label': '4D1', 'order': 4, 'powers': [4, 22, 21], 'representative': 43909200, 'size': 15}
  • id: 157604331
    {'aut_label': '4D-1', 'centralizer': '15.a1.a1', 'counter': 22, 'group_counter': 194, 'group_order': 2880, 'label': '4D-1', 'order': 4, 'powers': [4, 21, 22], 'representative': 119751120, 'size': 15}
  • id: 157604332
    {'aut_label': '4E', 'centralizer': '18.c1.a1', 'counter': 23, 'group_counter': 194, 'group_order': 2880, 'label': '4E', 'order': 4, 'powers': [2, 23, 23], 'representative': 1582, 'size': 18}
  • id: 157604333
    {'aut_label': '4F', 'centralizer': '30.c1.a1', 'counter': 24, 'group_counter': 194, 'group_order': 2880, 'label': '4F', 'order': 4, 'powers': [2, 24, 24], 'representative': 87091209, 'size': 30}
  • id: 157604334
    {'aut_label': '4G1', 'centralizer': '30.c1.a1', 'counter': 25, 'group_counter': 194, 'group_order': 2880, 'label': '4G1', 'order': 4, 'powers': [8, 26, 25], 'representative': 8023698, 'size': 30}
  • id: 157604335
    {'aut_label': '4G-1', 'centralizer': '30.c1.a1', 'counter': 26, 'group_counter': 194, 'group_order': 2880, 'label': '4G-1', 'order': 4, 'powers': [8, 25, 26], 'representative': 11612169, 'size': 30}
  • id: 157604336
    {'aut_label': '4H1', 'centralizer': '30.a1.a1', 'counter': 27, 'group_counter': 194, 'group_order': 2880, 'label': '4H1', 'order': 4, 'powers': [4, 28, 27], 'representative': 123419525, 'size': 30}
  • id: 157604337
    {'aut_label': '4H-1', 'centralizer': '30.a1.a1', 'counter': 28, 'group_counter': 194, 'group_order': 2880, 'label': '4H-1', 'order': 4, 'powers': [4, 27, 28], 'representative': 84188165, 'size': 30}
  • id: 157604338
    {'aut_label': '4I1', 'centralizer': '45.a1.a1', 'counter': 29, 'group_counter': 194, 'group_order': 2880, 'label': '4I1', 'order': 4, 'powers': [4, 30, 29], 'representative': 8023807, 'size': 45}
  • id: 157604340
    {'aut_label': '4I-1', 'centralizer': '45.a1.a1', 'counter': 30, 'group_counter': 194, 'group_order': 2880, 'label': '4I-1', 'order': 4, 'powers': [4, 29, 30], 'representative': 11612287, 'size': 45}
  • id: 157604341
    {'aut_label': '4J', 'centralizer': '90.c1.a1', 'counter': 31, 'group_counter': 194, 'group_order': 2880, 'label': '4J', 'order': 4, 'powers': [2, 31, 31], 'representative': 3669862, 'size': 90}
  • id: 157604342
    {'aut_label': '4K1', 'centralizer': '90.a1.a1', 'counter': 32, 'group_counter': 194, 'group_order': 2880, 'label': '4K1', 'order': 4, 'powers': [4, 33, 32], 'representative': 8025254, 'size': 90}
  • id: 157604343
    {'aut_label': '4K-1', 'centralizer': '90.a1.a1', 'counter': 33, 'group_counter': 194, 'group_order': 2880, 'label': '4K-1', 'order': 4, 'powers': [4, 32, 33], 'representative': 11613734, 'size': 90}
  • id: 157604344
    {'aut_label': '4L1', 'centralizer': '90.c1.a1', 'counter': 34, 'group_counter': 194, 'group_order': 2880, 'label': '4L1', 'order': 4, 'powers': [8, 35, 34], 'representative': 8023822, 'size': 90}
  • id: 157604345
    {'aut_label': '4L-1', 'centralizer': '90.c1.a1', 'counter': 35, 'group_counter': 194, 'group_order': 2880, 'label': '4L-1', 'order': 4, 'powers': [8, 34, 35], 'representative': 11612297, 'size': 90}
  • id: 157604346
    {'aut_label': '5A', 'centralizer': '4.b1.a1', 'counter': 36, 'group_counter': 194, 'group_order': 2880, 'label': '5A', 'order': 5, 'powers': [36, 36, 1], 'representative': 170916480, 'size': 4}
  • id: 157604347
    {'aut_label': '6A', 'centralizer': '6.p1.a1', 'counter': 37, 'group_counter': 194, 'group_order': 2880, 'label': '6A', 'order': 6, 'powers': [13, 2, 37], 'representative': 856, 'size': 6}
  • id: 157604348
    {'aut_label': '6B', 'centralizer': '10.d1.a1', 'counter': 38, 'group_counter': 194, 'group_order': 2880, 'label': '6B', 'order': 6, 'powers': [13, 4, 38], 'representative': 3670560, 'size': 10}
  • id: 157604349
    {'aut_label': '6C', 'centralizer': '12.p1.a1', 'counter': 39, 'group_counter': 194, 'group_order': 2880, 'label': '6C', 'order': 6, 'powers': [13, 5, 39], 'representative': 1441, 'size': 12}
  • id: 157604351
    {'aut_label': '6D', 'centralizer': '24.cd1.a1', 'counter': 40, 'group_counter': 194, 'group_order': 2880, 'label': '6D', 'order': 6, 'powers': [14, 3, 40], 'representative': 1572, 'size': 24}
  • id: 157604352
    {'aut_label': '6E', 'centralizer': '30.o1.a1', 'counter': 41, 'group_counter': 194, 'group_order': 2880, 'label': '6E', 'order': 6, 'powers': [13, 8, 41], 'representative': 3670576, 'size': 30}
  • id: 157604353
    {'aut_label': '6F', 'centralizer': '40.i1.a1', 'counter': 42, 'group_counter': 194, 'group_order': 2880, 'label': '6F', 'order': 6, 'powers': [14, 4, 42], 'representative': 3669124, 'size': 40}
  • id: 157604354
    {'aut_label': '6G', 'centralizer': '60.j1.a1', 'counter': 43, 'group_counter': 194, 'group_order': 2880, 'label': '6G', 'order': 6, 'powers': [13, 10, 43], 'representative': 87092042, 'size': 60}
  • id: 157604355
    {'aut_label': '6H', 'centralizer': '80.g1.a1', 'counter': 44, 'group_counter': 194, 'group_order': 2880, 'label': '6H', 'order': 6, 'powers': [15, 4, 44], 'representative': 3670568, 'size': 80}
  • id: 157604356
    {'aut_label': '6I', 'centralizer': '120.cc1.a1', 'counter': 45, 'group_counter': 194, 'group_order': 2880, 'label': '6I', 'order': 6, 'powers': [14, 7, 45], 'representative': 87091339, 'size': 120}
  • id: 157604357
    {'aut_label': '10A', 'centralizer': '12.bp1.a1', 'counter': 46, 'group_counter': 194, 'group_order': 2880, 'label': '10A', 'order': 10, 'powers': [36, 46, 2], 'representative': 50803216, 'size': 12}
  • id: 157604358
    {'aut_label': '10B', 'centralizer': '12.bn1.a1', 'counter': 47, 'group_counter': 194, 'group_order': 2880, 'label': '10B', 'order': 10, 'powers': [36, 47, 3], 'representative': 50804760, 'size': 12}
  • id: 157604359
    {'aut_label': '10C', 'centralizer': '24.i1.a1', 'counter': 48, 'group_counter': 194, 'group_order': 2880, 'label': '10C', 'order': 10, 'powers': [36, 48, 5], 'representative': 127774081, 'size': 24}
  • id: 157604360
    {'aut_label': '10D', 'centralizer': '36.bi1.a1', 'counter': 49, 'group_counter': 194, 'group_order': 2880, 'label': '10D', 'order': 10, 'powers': [36, 49, 6], 'representative': 50803327, 'size': 36}
  • id: 157604362
    {'aut_label': '10E', 'centralizer': '72.c1.a1', 'counter': 50, 'group_counter': 194, 'group_order': 2880, 'label': '10E', 'order': 10, 'powers': [36, 50, 9], 'representative': 80237521, 'size': 72}
  • id: 157604363
    {'aut_label': '12A1', 'centralizer': '10.d1.a1', 'counter': 51, 'group_counter': 194, 'group_order': 2880, 'label': '12A1', 'order': 12, 'powers': [38, 16, 51], 'representative': 8024520, 'size': 10}
  • id: 157604364
    {'aut_label': '12A-1', 'centralizer': '10.d1.a1', 'counter': 52, 'group_counter': 194, 'group_order': 2880, 'label': '12A-1', 'order': 12, 'powers': [38, 17, 52], 'representative': 11613000, 'size': 10}
  • id: 157604365
    {'aut_label': '12B', 'centralizer': '12.bc1.a1', 'counter': 53, 'group_counter': 194, 'group_order': 2880, 'label': '12B', 'order': 12, 'powers': [37, 18, 53], 'representative': 1449, 'size': 12}
  • id: 157604366
    {'aut_label': '12C1', 'centralizer': '30.o1.a1', 'counter': 54, 'group_counter': 194, 'group_order': 2880, 'label': '12C1', 'order': 12, 'powers': [38, 19, 54], 'representative': 8024527, 'size': 30}
  • id: 157604367
    {'aut_label': '12C-1', 'centralizer': '30.o1.a1', 'counter': 55, 'group_counter': 194, 'group_order': 2880, 'label': '12C-1', 'order': 12, 'powers': [38, 20, 55], 'representative': 11613007, 'size': 30}
  • id: 157604368
    {'aut_label': '12D1', 'centralizer': '40.i1.a1', 'counter': 56, 'group_counter': 194, 'group_order': 2880, 'label': '12D1', 'order': 12, 'powers': [42, 16, 56], 'representative': 8023683, 'size': 40}
  • id: 157604369
    {'aut_label': '12D-1', 'centralizer': '40.i1.a1', 'counter': 57, 'group_counter': 194, 'group_order': 2880, 'label': '12D-1', 'order': 12, 'powers': [42, 17, 57], 'representative': 11612163, 'size': 40}
  • id: 157604370
    {'aut_label': '12E', 'centralizer': '60.w1.a1', 'counter': 58, 'group_counter': 194, 'group_order': 2880, 'label': '12E', 'order': 12, 'powers': [37, 24, 58], 'representative': 87092058, 'size': 60}
  • id: 157604371
    {'aut_label': '12F1', 'centralizer': '60.w1.a1', 'counter': 59, 'group_counter': 194, 'group_order': 2880, 'label': '12F1', 'order': 12, 'powers': [41, 25, 59], 'representative': 11613009, 'size': 60}
  • id: 157604373
    {'aut_label': '12F-1', 'centralizer': '60.w1.a1', 'counter': 60, 'group_counter': 194, 'group_order': 2880, 'label': '12F-1', 'order': 12, 'powers': [41, 26, 60], 'representative': 8025138, 'size': 60}
  • id: 157604374
    {'aut_label': '12G1', 'centralizer': '60.j1.a1', 'counter': 61, 'group_counter': 194, 'group_order': 2880, 'label': '12G1', 'order': 12, 'powers': [38, 27, 61], 'representative': 84189005, 'size': 60}
  • id: 157604375
    {'aut_label': '12G-1', 'centralizer': '60.j1.a1', 'counter': 62, 'group_counter': 194, 'group_order': 2880, 'label': '12G-1', 'order': 12, 'powers': [38, 28, 62], 'representative': 123420965, 'size': 60}
  • id: 157604376
    {'aut_label': '12H1', 'centralizer': '80.g1.a1', 'counter': 63, 'group_counter': 194, 'group_order': 2880, 'label': '12H1', 'order': 12, 'powers': [44, 16, 63], 'representative': 8024532, 'size': 80}
  • id: 157604377
    {'aut_label': '12H-1', 'centralizer': '80.g1.a1', 'counter': 64, 'group_counter': 194, 'group_order': 2880, 'label': '12H-1', 'order': 12, 'powers': [44, 17, 64], 'representative': 11613608, 'size': 80}
  • id: 157604378
    {'aut_label': '12I1', 'centralizer': '120.cc1.a1', 'counter': 65, 'group_counter': 194, 'group_order': 2880, 'label': '12I1', 'order': 12, 'powers': [42, 21, 65], 'representative': 119751140, 'size': 120}
  • id: 157604379
    {'aut_label': '12I-1', 'centralizer': '120.cc1.a1', 'counter': 66, 'group_counter': 194, 'group_order': 2880, 'label': '12I-1', 'order': 12, 'powers': [42, 22, 66], 'representative': 43909215, 'size': 120}
  • id: 157604380
    {'aut_label': '15A', 'centralizer': '8.c1.a1', 'counter': 67, 'group_counter': 194, 'group_order': 2880, 'label': '15A', 'order': 15, 'powers': [67, 36, 13], 'representative': 170917920, 'size': 8}
  • id: 157604381
    {'aut_label': '15B', 'centralizer': '32.a1.a1', 'counter': 68, 'group_counter': 194, 'group_order': 2880, 'label': '15B', 'order': 15, 'powers': [68, 36, 14], 'representative': 80236812, 'size': 32}
  • id: 157604382
    {'aut_label': '15C', 'centralizer': '64.a1.a1', 'counter': 69, 'group_counter': 194, 'group_order': 2880, 'label': '15C', 'order': 15, 'powers': [69, 36, 15], 'representative': 170917340, 'size': 64}
  • id: 157604384
    {'aut_label': '20A', 'centralizer': '24.l1.a1', 'counter': 70, 'group_counter': 194, 'group_order': 2880, 'label': '20A', 'order': 20, 'powers': [46, 70, 18], 'representative': 127774098, 'size': 24}
  • id: 157604385
    {'aut_label': '20B', 'centralizer': '72.f1.a1', 'counter': 71, 'group_counter': 194, 'group_order': 2880, 'label': '20B', 'order': 20, 'powers': [46, 71, 23], 'representative': 50804782, 'size': 72}
  • id: 157604386
    {'aut_label': '30A', 'centralizer': '24.bt1.a1', 'counter': 72, 'group_counter': 194, 'group_order': 2880, 'label': '30A', 'order': 30, 'powers': [67, 46, 37], 'representative': 170917936, 'size': 24}
  • id: 157604387
    {'aut_label': '30B', 'centralizer': '48.h1.a1', 'counter': 73, 'group_counter': 194, 'group_order': 2880, 'label': '30B', 'order': 30, 'powers': [67, 48, 39], 'representative': 50804041, 'size': 48}
  • id: 157604388
    {'aut_label': '30C', 'centralizer': '96.e1.a1', 'counter': 74, 'group_counter': 194, 'group_order': 2880, 'label': '30C', 'order': 30, 'powers': [68, 47, 40], 'representative': 170918048, 'size': 96}
  • id: 157604389
    {'aut_label': '60A', 'centralizer': '48.p1.a1', 'counter': 75, 'group_counter': 194, 'group_order': 2880, 'label': '60A', 'order': 60, 'powers': [72, 70, 53], 'representative': 50804049, 'size': 48}
• gps_qchar •

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

  
  
  • id: 15393618
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15393629
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 15393640
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 15393651
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 15393662
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 15393673
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 15393675
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 15393676
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 15393677
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 2, 2, -2, -2, -2], 'schur_index': 1}
  • id: 15393619
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, 2, 2, -2, 2], 'schur_index': 1}
  • id: 15393620
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, -2, -2, 2, -2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, -2, 2, -2], 'schur_index': 1}
  • id: 15393621
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 15393622
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, -1, 2, -1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 0, -1, 2, -1, -1, 0, 2, 0, 2, 0, 0, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, 2, -1, 2, 0, -1, -1, 0, -1], 'schur_index': 1}
  • id: 15393623
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, -1, -1, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, -1, 2, -1, 0, -1, -1, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, -1, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 0, 0, 2, 0, -1, 0], 'schur_index': 1}
  • id: 15393624
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 0, -2, -2, 2, 0, 0, -2, 0, 2, -1, -1, -2, -2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, -1, 0, -1, 1, 2, -2, 0, -2, 0, -2, -2, 0, -2, -2, 1, 1, 0, 0, 0, 0, 0, 1, 1, -1, -1, 2, -1, -1, 0, 0, 2, 0, 1, 0], 'schur_index': 1}
  • id: 15393625
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 0, -2, -2, 2, 0, 0, -2, 0, 2, -1, -1, 2, 2, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, -1, 0, -1, 1, 2, -2, 0, -2, 0, 2, 2, 0, 2, 2, -1, -1, 0, 0, 0, 0, 0, -1, -1, 1, 1, 2, -1, -1, 0, 0, 2, 0, 1, 0], 'schur_index': 1}
  • id: 15393626
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, -2, 0, 0, 2, 0, -2, 0, 0, -1, 2, -1, -2, -2, -2, -2, -2, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 1, 0, -1, 2, 1, -1, 0, 2, 0, -2, 0, 0, 1, 1, 1, 1, 1, -2, -2, -1, -1, 1, -1, -1, 1, 1, 0, 0, -1, 2, -1, -2, 0, -1, 1, 0, 1], 'schur_index': 1}
  • id: 15393627
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, -2, 0, 0, 2, 0, -2, 0, 0, -1, 2, -1, 2, 2, -2, 2, 2, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 1, 0, -1, 2, 1, -1, 0, 2, 0, -2, 0, 0, -1, -1, 1, -1, -1, 2, 2, 1, 1, 1, 1, 1, -1, -1, 0, 0, -1, 2, -1, -2, 0, -1, 1, 0, 1], 'schur_index': 1}
  • id: 15393628
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, -1, 2, -1, -2, -2, 2, -2, -2, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 0, -1, 2, -1, -1, 0, 2, 0, 2, 0, 0, 1, 1, -1, 1, 1, -2, -2, 1, 1, -1, 1, 1, 1, 1, 0, 0, -1, 2, -1, 2, 0, -1, -1, 0, -1], 'schur_index': 1}
  • id: 15393630
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, -1, -1, -2, -2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 0, -1, 2, -1, 0, -1, -1, 2, 2, 0, 2, 0, -2, -2, 0, -2, -2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, -1, -1, 0, 0, 2, 0, -1, 0], 'schur_index': 1}
  • id: 15393635
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, -1, 3, 3, 1, -1, 3, -1, 1, 1, -1, 1, 3, 0, 0, 3, 3, -1, -1, -1, 3, 3, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 3, -1, 3, 1, 0, -1, 0, 1, 0, 0, -1, 3, 1, -1, 1, 3, 3, -1, -1, -1, 0, 0, 1, -1, -1, 1, -1, 0, 0, 0, 0, 3, 0, 0, -1, -1, -1, 1, 0, -1], 'schur_index': 1}
  • id: 15393636
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, 3, 3, -1, -1, 3, -1, -1, -1, -1, -1, 3, 0, 0, 3, 3, 1, -1, -1, 3, 3, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 3, -1, 3, -1, 0, -1, 0, -1, 0, 0, -1, 3, -1, -1, -1, 3, 3, 1, -1, -1, 0, 0, -1, 1, 1, -1, 1, 0, 0, 0, 0, 3, 0, 0, 1, 1, -1, -1, 0, 1], 'schur_index': 1}
  • id: 15393637
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, -3, 3, -1, 1, -3, -1, 1, -1, 1, 1, 3, 0, 0, -3, -3, 1, 1, 1, 3, 3, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 3, -1, 3, -1, 0, -1, 0, -1, 0, 0, -1, -3, -1, 1, 1, -3, -3, 1, 1, 1, 0, 0, 1, -1, 1, 1, -1, 0, 0, 0, 0, 3, 0, 0, 1, -1, -1, -1, 0, 1], 'schur_index': 1}
  • id: 15393638
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, -3, 3, -1, 1, -3, -1, 1, -1, 1, 1, 3, 0, 0, 3, 3, 1, -1, -1, -3, -3, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 3, -1, 3, -1, 0, -1, 0, -1, 0, 0, -1, -3, -1, 1, 1, 3, 3, 1, -1, -1, 0, 0, -1, 1, 1, -1, 1, 0, 0, 0, 0, 3, 0, 0, 1, -1, -1, -1, 0, 1], 'schur_index': 1}
  • id: 15393639
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, -3, 3, 1, 1, -3, -1, -1, 1, 1, -1, 3, 0, 0, -3, -3, -1, 1, 1, 3, 3, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 3, -1, 3, 1, 0, -1, 0, 1, 0, 0, -1, -3, 1, 1, -1, -3, -3, -1, 1, 1, 0, 0, -1, 1, -1, -1, 1, 0, 0, 0, 0, 3, 0, 0, -1, 1, -1, 1, 0, -1], 'schur_index': 1}
  • id: 15393641
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, -3, 3, 1, 1, -3, -1, -1, 1, 1, -1, 3, 0, 0, 3, 3, -1, -1, -1, -3, -3, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 3, -1, 3, 1, 0, -1, 0, 1, 0, 0, -1, -3, 1, 1, -1, 3, 3, -1, -1, -1, 0, 0, 1, -1, -1, 1, -1, 0, 0, 0, 0, 3, 0, 0, -1, 1, -1, 1, 0, -1], 'schur_index': 1}
  • id: 15393642
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, 3, 3, -1, -1, 3, -1, -1, -1, -1, -1, 3, 0, 0, -3, -3, 1, 1, 1, -3, -3, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 3, -1, 3, -1, 0, -1, 0, -1, 0, 0, -1, 3, -1, -1, -1, -3, -3, 1, 1, 1, 0, 0, 1, -1, 1, 1, -1, 0, 0, 0, 0, 3, 0, 0, 1, 1, -1, -1, 0, 1], 'schur_index': 1}
  • id: 15393643
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, 3, 3, 1, -1, 3, -1, 1, 1, -1, 1, 3, 0, 0, -3, -3, -1, 1, 1, -3, -3, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 3, -1, 3, 1, 0, -1, 0, 1, 0, 0, -1, 3, 1, -1, 1, -3, -3, -1, 1, 1, 0, 0, -1, 1, -1, -1, 1, 0, 0, 0, 0, 3, 0, 0, -1, -1, -1, 1, 0, -1], 'schur_index': 1}
  • id: 15393631
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2i', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, -4, 4, -4, 0, 0, 4, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 0, 2, -4, 2, 0, 2, -2, 4, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 4, 0, 2, 0], 'schur_index': 1}
  • id: 15393632
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2j', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, 0, -4, -4, 0, 0, -4, 0, 4, 0, 0, -2, 4, -2, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 2, 2, 0, 2, -4, -2, 2, 0, 4, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 4, -2, -4, 0, -2, 2, 0, 2], 'schur_index': 1}
  • id: 15393633
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2k', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, 0, -4, 4, 0, 0, -4, 0, -4, 0, 0, -2, 4, -2, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 2, -2, 0, 2, -4, 2, 2, 0, 4, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, 0, -2, -2, 0, -2], 'schur_index': 1}
  • id: 15393634
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.2l', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 0, 4, -4, -4, 0, 0, -4, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 0, -2, -4, 2, 0, 2, 2, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 4, 0, -2, 0], 'schur_index': 1}
  • id: 15393648
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 4, 4, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 4, 4, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 15393649
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, -2, -2, 1, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, -2, -2, 0, 1, 0, 4, 0, 0, 0, 0, -2, -2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, -2, -2, 1, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 15393650
    {'cdim': 4, 'counter': 39, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.4c', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, -4, 0, -4, -4, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, -4, -4, 0, 0, 0, 0, 0, -1, 1, 1, 1, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 15393652
    {'cdim': 4, 'counter': 40, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.4d', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 4, -4, 0, 0, -4, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 4, -4, 0, 0, 0, 0, 0, -1, 1, -1, 1, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 15393653
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.4e', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 0, -4, 4, 0, 0, -4, 0, 0, 0, 4, 4, 4, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, -4, 4, 0, 0, 0, 0, 0, -1, -1, 1, -1, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 15393654
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, -2, -2, 1, -4, -4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, -2, -2, 0, 1, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, 0, 0, -2, -2, 1, 0, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 15393644
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3i', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -2, -6, -6, -2, 2, 6, 2, 2, 2, -2, -2, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, -2, -6, -2, 0, 2, 0, 2, 0, 0, -2, -6, -2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, -2, -2, -2, 0, 2], 'schur_index': 1}
  • id: 15393645
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3j', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -2, -6, -6, 2, 2, 6, 2, -2, -2, -2, 2, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 6, -2, -6, 2, 0, 2, 0, -2, 0, 0, -2, -6, 2, 2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, -2, 2, -2, 2, 0, -2], 'schur_index': 1}
  • id: 15393646
    {'cdim': 3, 'counter': 35, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3k', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -2, 6, -6, -2, -2, -6, 2, -2, 2, 2, 2, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 6, -2, -6, -2, 0, 2, 0, 2, 0, 0, -2, 6, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 2, -2, -2, 0, 2], 'schur_index': 1}
  • id: 15393647
    {'cdim': 3, 'counter': 36, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.3l', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -2, 6, -6, 2, -2, -6, 2, 2, -2, 2, -2, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, -2, -6, 2, 0, 2, 0, -2, 0, 0, -2, 6, 2, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, -2, -2, -2, 2, 0, -2], 'schur_index': 1}
  • id: 15393656
    {'cdim': 6, 'counter': 44, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.6a', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, -2, 0, 6, 2, 0, 0, -2, 0, 2, 0, 0, -3, 0, 0, 6, 6, -2, -2, -2, 0, 0, 0, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 6, 1, -3, -1, 0, 1, 0, -1, 0, 0, -2, 0, 2, 0, 0, -3, -3, 1, 1, 1, 0, 0, -1, 1, 1, -1, 1, 0, 0, 0, 0, -3, 0, 0, -2, 0, 1, -1, 0, 1], 'schur_index': 1}
  • id: 15393657
    {'cdim': 6, 'counter': 45, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.6b', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, -2, 0, 6, -2, 0, 0, -2, 0, -2, 0, 0, -3, 0, 0, 6, 6, 2, -2, -2, 0, 0, 0, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 6, 1, -3, 1, 0, 1, 0, 1, 0, 0, -2, 0, -2, 0, 0, -3, -3, -1, 1, 1, 0, 0, 1, -1, -1, 1, -1, 0, 0, 0, 0, -3, 0, 0, 2, 0, 1, 1, 0, -1], 'schur_index': 1}
  • id: 15393658
    {'cdim': 6, 'counter': 46, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.6c', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -2, 0, 6, -2, 0, 0, -2, 0, -2, 0, 0, -3, 0, 0, -6, -6, 2, 2, 2, 0, 0, 0, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 6, 1, -3, 1, 0, 1, 0, 1, 0, 0, -2, 0, -2, 0, 0, 3, 3, -1, -1, -1, 0, 0, -1, 1, -1, -1, 1, 0, 0, 0, 0, -3, 0, 0, 2, 0, 1, 1, 0, -1], 'schur_index': 1}
  • id: 15393659
    {'cdim': 6, 'counter': 47, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.6d', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -2, 0, 6, 2, 0, 0, -2, 0, 2, 0, 0, -3, 0, 0, -6, -6, -2, 2, 2, 0, 0, 0, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 6, 1, -3, -1, 0, 1, 0, -1, 0, 0, -2, 0, 2, 0, 0, 3, 3, 1, -1, -1, 0, 0, 1, -1, 1, 1, -1, 0, 0, 0, 0, -3, 0, 0, -2, 0, 1, -1, 0, 1], 'schur_index': 1}
  • id: 15393655
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.4g', 'multiplicity': 2, 'nt': [24, 224], 'qdim': 8, 'qvalues': [8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, 4, 0, 0, 4, 4, 0, -2, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 0, 0, -4, 0, 0, 0], 'schur_index': 1}
  • id: 15393663
    {'cdim': 8, 'counter': 50, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.8a', 'multiplicity': 1, 'nt': [15, 11], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, 0, 1, 1, 0, 1], 'schur_index': 1}
  • id: 15393664
    {'cdim': 8, 'counter': 51, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.8b', 'multiplicity': 1, 'nt': [15, 11], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 8, 0, 0, -4, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, -2, 0, 1, 0], 'schur_index': 1}
  • id: 15393665
    {'cdim': 8, 'counter': 52, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.8c', 'multiplicity': 1, 'nt': [30, 51], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 8, 0, 0, 4, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, -2, 0, -1, 0], 'schur_index': 1}
  • id: 15393666
    {'cdim': 8, 'counter': 53, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.8d', 'multiplicity': 1, 'nt': [30, 51], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 2, 0, 1, -1, 0, -1], 'schur_index': 1}
  • id: 15393660
    {'cdim': 6, 'counter': 48, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.6e', 'multiplicity': 2, 'nt': [36, 801], 'qdim': 12, 'qvalues': [12, -4, 0, -12, -4, 0, 0, 4, 0, 4, 0, 0, -6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 2, 6, 2, 0, -2, 0, -2, 0, 0, -4, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -6, 0, 0, 4, 0, 2, 2, 0, -2], 'schur_index': 1}
  • id: 15393661
    {'cdim': 6, 'counter': 49, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.6f', 'multiplicity': 2, 'nt': [36, 801], 'qdim': 12, 'qvalues': [12, -4, 0, -12, 4, 0, 0, 4, 0, -4, 0, 0, -6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 2, 6, -2, 0, -2, 0, 2, 0, 0, -4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -6, 0, 0, -4, 0, 2, -2, 0, 2], 'schur_index': 1}
  • id: 15393667
    {'cdim': 12, 'counter': 54, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.12a', 'multiplicity': 1, 'nt': [20, 121], 'qdim': 12, 'qvalues': [12, -4, 12, 0, 4, -4, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, 4, 0, 0, 0, 0, 0, 0, 1, -3, -1, 1, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1, 1, 1, -1, 0, 1], 'schur_index': 1}
  • id: 15393668
    {'cdim': 12, 'counter': 55, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.12b', 'multiplicity': 1, 'nt': [30, 110], 'qdim': 12, 'qvalues': [12, -4, 12, 0, -4, -4, 0, 0, -4, 0, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, -4, 0, 0, 0, 0, 0, 0, 1, -3, 1, 1, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -1, -1, 1, 1, 0, -1], 'schur_index': 1}
  • id: 15393669
    {'cdim': 12, 'counter': 56, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.12c', 'multiplicity': 1, 'nt': [30, 213], 'qdim': 12, 'qvalues': [12, -4, -12, 0, -4, 4, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, -4, 0, 0, 0, 0, 0, 0, 1, 3, 1, -1, -1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -1, 1, 1, 1, 0, -1], 'schur_index': 1}
  • id: 15393670
    {'cdim': 12, 'counter': 57, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.12d', 'multiplicity': 1, 'nt': [30, 213], 'qdim': 12, 'qvalues': [12, -4, -12, 0, 4, 4, 0, 0, -4, 0, 0, 0, 12, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, 4, 0, 0, 0, 0, 0, 0, 1, 3, -1, -1, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1, -1, 1, -1, 0, 1], 'schur_index': 1}
  • id: 15393671
    {'cdim': 16, 'counter': 58, 'faithful': False, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.16a', 'multiplicity': 1, 'nt': [30, 161], 'qdim': 16, 'qvalues': [16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, 0, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 15393672
    {'cdim': 24, 'counter': 59, 'faithful': True, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.24a', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, -1, 1, 0, -1], 'schur_index': 1}
  • id: 15393674
    {'cdim': 24, 'counter': 60, 'faithful': True, 'group': '2880.hl', 'group_order': 2880, 'image': None, 'label': '2880.hl.24b', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, -1, -1, 0, 1], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 35238106
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 2880, 'label': '2880.hl.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35238117
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 1440, 'label': '2880.hl.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35238128
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 1440, 'label': '2880.hl.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35238139
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 1440, 'label': '2880.hl.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 35238150
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 1440, 'label': '2880.hl.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 35238161
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 1440, 'label': '2880.hl.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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: 35238172
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 1440, 'label': '2880.hl.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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: 35238179
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 1440, 'label': '2880.hl.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 35238180
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.k1.a1', 'kernel_order': 720, 'label': '2880.hl.1i1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35238107
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.k1.a1', 'kernel_order': 720, 'label': '2880.hl.1i2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35238108
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.j1.a1', 'kernel_order': 720, 'label': '2880.hl.1j1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 35238109
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.j1.a1', 'kernel_order': 720, 'label': '2880.hl.1j2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 35238110
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 720, 'label': '2880.hl.1k1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 35238111
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 720, 'label': '2880.hl.1k2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 35238112
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 720, 'label': '2880.hl.1l1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35238113
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2880, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 720, 'label': '2880.hl.1l2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35238114
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 480, 'label': '2880.hl.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238115
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 480, 'label': '2880.hl.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35238116
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 240, 'label': '2880.hl.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35238118
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 240, 'label': '2880.hl.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35238119
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.f1.a1', 'kernel_order': 240, 'label': '2880.hl.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238120
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 240, 'label': '2880.hl.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238121
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 240, 'label': '2880.hl.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238122
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 240, 'label': '2880.hl.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35238123
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 25, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.e1.a1', 'kernel_order': 120, 'label': '2880.hl.2i1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35238124
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 26, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.e1.a1', 'kernel_order': 120, 'label': '2880.hl.2i2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35238125
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 27, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.a1', 'kernel_order': 120, 'label': '2880.hl.2j1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[2, 1]], [[-2, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238126
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 28, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.a1', 'kernel_order': 120, 'label': '2880.hl.2j2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[2, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238127
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 29, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.a1', 'kernel_order': 120, 'label': '2880.hl.2k1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[2, 1]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238129
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 480, 'counter': 30, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1.a1', 'kernel_order': 120, 'label': '2880.hl.2k2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238130
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 31, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 120, 'label': '2880.hl.2l1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35238131
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 480, 'counter': 32, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 120, 'label': '2880.hl.2l2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35238132
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  • id: 35238133
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.g1.a1', 'kernel_order': 120, 'label': '2880.hl.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238134
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 35, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 60, 'label': '2880.hl.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238135
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 36, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 60, 'label': '2880.hl.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238136
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 37, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 60, 'label': '2880.hl.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238137
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 60, 'label': '2880.hl.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238138
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 39, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 60, 'label': '2880.hl.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238140
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 40, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 60, 'label': '2880.hl.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238141
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 41, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.c1.a1', 'kernel_order': 30, 'label': '2880.hl.3i1', 'nt': [12, 53], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-3, 1]], [[3, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[-3, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238142
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 42, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.c1.a1', 'kernel_order': 30, 'label': '2880.hl.3i2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[3, 1]], [[-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 1]], [[3, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238143
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 43, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.c1.a1', 'kernel_order': 30, 'label': '2880.hl.3j1', 'nt': [12, 53], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-3, 1]], [[3, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[-3, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238144
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 44, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.c1.a1', 'kernel_order': 30, 'label': '2880.hl.3j2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[3, 1]], [[-3, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 1]], [[3, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238145
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 45, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 30, 'label': '2880.hl.3k1', 'nt': [12, 53], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[3, 1]], [[-3, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[-3, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238146
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 46, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 30, 'label': '2880.hl.3k2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-3, 1]], [[3, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 1]], [[3, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238147
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 47, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 30, 'label': '2880.hl.3l1', 'nt': [12, 53], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[3, 1]], [[-3, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[-3, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238148
    {'center': '24.g1.a1', 'center_index': 24, 'center_order': 120, 'counter': 48, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 30, 'label': '2880.hl.3l2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-3, 1]], [[3, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 1]], [[3, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238149
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 144, 'counter': 49, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 144, 'label': '2880.hl.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35238151
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 80, 'counter': 50, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 80, 'label': '2880.hl.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35238152
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 144, 'counter': 51, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.c1.a1', 'kernel_order': 72, 'label': '2880.hl.4c', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35238153
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 144, 'counter': 52, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.a1', 'kernel_order': 72, 'label': '2880.hl.4d', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 35238154
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 144, 'counter': 53, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1.a1', 'kernel_order': 72, 'label': '2880.hl.4e', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 35238155
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 80, 'counter': 54, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 40, 'label': '2880.hl.4f', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35238156
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 80, 'counter': 55, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '144.143', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 20, 'label': '2880.hl.4g1', 'nt': [24, 224], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[0, 0]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35238157
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 80, 'counter': 56, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '144.143', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 20, 'label': '2880.hl.4g2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35238158
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 57, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 20, 'label': '2880.hl.6a', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[6, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238159
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 58, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 20, 'label': '2880.hl.6b', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[6, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238160
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 59, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 10, 'label': '2880.hl.6c', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[6, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238162
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 60, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 10, 'label': '2880.hl.6d', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[6, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238163
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 61, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '576.8311', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 5, 'label': '2880.hl.6e1', 'nt': [36, 801], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238164
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 62, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '576.8311', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 5, 'label': '2880.hl.6e2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238165
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 63, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '576.8311', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 5, 'label': '2880.hl.6f1', 'nt': [36, 801], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238166
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 20, 'counter': 64, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '576.8311', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 5, 'label': '2880.hl.6f2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238167
    {'center': '120.b1.a1', 'center_index': 120, 'center_order': 24, 'counter': 65, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '120.36', 'image_order': 120, 'indicator': 1, 'kernel': '120.b1.a1', 'kernel_order': 24, 'label': '2880.hl.8a', 'nt': [15, 11], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238168
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 24, 'counter': 66, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '120.36', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 24, 'label': '2880.hl.8b', 'nt': [15, 11], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 35238169
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 24, 'counter': 67, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '240.195', 'image_order': 240, 'indicator': 1, 'kernel': '240.a1.a1', 'kernel_order': 12, 'label': '2880.hl.8c', 'nt': [30, 51], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 35238170
    {'center': '120.b1.a1', 'center_index': 120, 'center_order': 24, 'counter': 68, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '240.195', 'image_order': 240, 'indicator': 1, 'kernel': '240.b1.a1', 'kernel_order': 12, 'label': '2880.hl.8d', 'nt': [30, 51], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238171
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 6, 'counter': 69, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '480.1189', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 6, 'label': '2880.hl.12a', 'nt': [20, 121], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238173
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 6, 'counter': 70, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '480.1189', 'image_order': 480, 'indicator': 1, 'kernel': '480.a1.a1', 'kernel_order': 6, 'label': '2880.hl.12b', 'nt': [30, 110], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238174
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 6, 'counter': 71, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '960.11361', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 3, 'label': '2880.hl.12c', 'nt': [30, 213], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238175
    {'center': '480.a1.a1', 'center_index': 480, 'center_order': 6, 'counter': 72, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '960.11361', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 3, 'label': '2880.hl.12d', 'nt': [30, 213], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-12, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 35238176
    {'center': '720.a1.a1', 'center_index': 720, 'center_order': 4, 'counter': 73, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '720.783', 'image_order': 720, 'indicator': 1, 'kernel': '720.a1.a1', 'kernel_order': 4, 'label': '2880.hl.16a', 'nt': [30, 161], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35238177
    {'center': '2880.a1.a1', 'center_index': 2880, 'center_order': 1, 'counter': 74, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2880.hl', 'image_order': 2880, 'indicator': 1, 'kernel': '2880.a1.a1', 'kernel_order': 1, 'label': '2880.hl.24a', 'nt': [60, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 35238178
    {'center': '2880.a1.a1', 'center_index': 2880, 'center_order': 1, 'counter': 75, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '2880.hl', 'group_counter': 194, 'group_order': 2880, 'image': None, 'image_isoclass': '2880.hl', 'image_order': 2880, 'indicator': 1, 'kernel': '2880.a1.a1', 'kernel_order': 1, 'label': '2880.hl.24b', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 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: 183536081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2880, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '2880.hl.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2880.hl', 'subgroup_hash': 799193401477229059, 'subgroup_order': 2880, 'subgroup_tex': 'S_3\\times F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1440, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5871', 'subgroup_hash': 5871, 'subgroup_order': 1440, 'subgroup_tex': 'S_3\\times D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1440, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5870', 'subgroup_hash': 5870, 'subgroup_order': 1440, 'subgroup_tex': 'S_3\\times A_4\\times F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1440, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5869', 'subgroup_hash': 5869, 'subgroup_order': 1440, 'subgroup_tex': 'S_3\\times A_4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1440, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5865', 'subgroup_hash': 5865, 'subgroup_order': 1440, 'subgroup_tex': 'C_3\\times F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1440, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5867', 'subgroup_hash': 5867, 'subgroup_order': 1440, 'subgroup_tex': 'C_{15}:C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1440, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5866', 'subgroup_hash': 5866, 'subgroup_order': 1440, 'subgroup_tex': 'F_5\\times C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1440, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5868', 'subgroup_hash': 5868, 'subgroup_order': 1440, 'subgroup_tex': 'C_{15}:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 183536969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 480, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '960.11361', 'subgroup_hash': 11361, 'subgroup_order': 960, 'subgroup_tex': 'C_2\\times F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 480, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '960.11038', 'subgroup_hash': 11038, 'subgroup_order': 960, 'subgroup_tex': 'S_3\\times D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '720.797', 'subgroup_hash': 797, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 720, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.792', 'subgroup_hash': 792, 'subgroup_order': 720, 'subgroup_tex': 'C_5\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.793', 'subgroup_hash': 793, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times C_5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 720, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '720.791', 'subgroup_hash': 791, 'subgroup_order': 720, 'subgroup_tex': 'C_3\\times D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '720.796', 'subgroup_hash': 796, 'subgroup_order': 720, 'subgroup_tex': 'D_5\\times C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 720, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.789', 'subgroup_hash': 789, 'subgroup_order': 720, 'subgroup_tex': 'C_3\\times A_4\\times F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536159
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.790', 'subgroup_hash': 790, 'subgroup_order': 720, 'subgroup_tex': 'A_4\\times C_{15}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 720, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.787', 'subgroup_hash': 787, 'subgroup_order': 720, 'subgroup_tex': 'C_3\\times A_4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.788', 'subgroup_hash': 788, 'subgroup_order': 720, 'subgroup_tex': '(A_4\\times C_{15}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.794', 'subgroup_hash': 794, 'subgroup_order': 720, 'subgroup_tex': 'S_4\\times D_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 183536204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 720, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '720.795', 'subgroup_hash': 795, 'subgroup_order': 720, 'subgroup_tex': 'D_{15}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 120, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.4.l1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '720.783', 'subgroup_hash': 783, 'subgroup_order': 720, 'subgroup_tex': 'F_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '2880.hl.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.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': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8311', 'subgroup_hash': 8311, 'subgroup_order': 576, 'subgroup_tex': 'C_4\\times S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 480, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.1197', 'subgroup_hash': 1197, 'subgroup_order': 480, 'subgroup_tex': 'C_2\\times D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 480, 'counter': 25, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2880.hl.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.1189', 'subgroup_hash': 1189, 'subgroup_order': 480, 'subgroup_tex': 'F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 120, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '480.1197', 'subgroup_hash': 1197, 'subgroup_order': 480, 'subgroup_tex': 'C_2\\times D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1011', 'subgroup_hash': 1011, 'subgroup_order': 480, 'subgroup_tex': 'D_{10}:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 120, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '480.994', 'subgroup_hash': 994, 'subgroup_order': 480, 'subgroup_tex': 'D_{15}:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '480.996', 'subgroup_hash': 996, 'subgroup_order': 480, 'subgroup_tex': 'C_{20}:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '480.1010', 'subgroup_hash': 1010, 'subgroup_order': 480, 'subgroup_tex': 'C_3:D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '480.1012', 'subgroup_hash': 1012, 'subgroup_order': 480, 'subgroup_tex': 'C_{15}:(C_4\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 183536326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.995', 'subgroup_hash': 995, 'subgroup_order': 480, 'subgroup_tex': 'F_5\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.997', 'subgroup_hash': 997, 'subgroup_order': 480, 'subgroup_tex': 'D_{60}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1193', 'subgroup_hash': 1193, 'subgroup_order': 480, 'subgroup_tex': 'D_{10}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1192', 'subgroup_hash': 1192, 'subgroup_order': 480, 'subgroup_tex': 'C_2\\times A_4\\times F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1191', 'subgroup_hash': 1191, 'subgroup_order': 480, 'subgroup_tex': 'D_{10}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1097', 'subgroup_hash': 1097, 'subgroup_order': 480, 'subgroup_tex': 'D_{12}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1011', 'subgroup_hash': 1011, 'subgroup_order': 480, 'subgroup_tex': 'D_{10}:C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 240, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1054', 'subgroup_hash': 1054, 'subgroup_order': 480, 'subgroup_tex': 'D_{20}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1067', 'subgroup_hash': 1067, 'subgroup_order': 480, 'subgroup_tex': 'C_{15}:C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1189', 'subgroup_hash': 1189, 'subgroup_order': 480, 'subgroup_tex': 'F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1010', 'subgroup_hash': 1010, 'subgroup_order': 480, 'subgroup_tex': 'C_3:D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1012', 'subgroup_hash': 1012, 'subgroup_order': 480, 'subgroup_tex': 'C_{15}:(C_4\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 183536459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1189', 'subgroup_hash': 1189, 'subgroup_order': 480, 'subgroup_tex': 'F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 240, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1189', 'subgroup_hash': 1189, 'subgroup_order': 480, 'subgroup_tex': 'F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 80, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.6.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1189', 'subgroup_hash': 1189, 'subgroup_order': 480, 'subgroup_tex': 'F_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 360, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.143', 'subgroup_hash': 143, 'subgroup_order': 360, 'subgroup_tex': 'C_5\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536503
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 360, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '360.142', 'subgroup_hash': 142, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 360, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.138', 'subgroup_hash': 138, 'subgroup_order': 360, 'subgroup_tex': 'C_{15}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 360, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.144', 'subgroup_hash': 144, 'subgroup_order': 360, 'subgroup_tex': 'A_4\\times D_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 183536537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 360, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.140', 'subgroup_hash': 140, 'subgroup_order': 360, 'subgroup_tex': 'C_{15}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 360, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.139', 'subgroup_hash': 139, 'subgroup_order': 360, 'subgroup_tex': 'C_{15}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 360, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.141', 'subgroup_hash': 141, 'subgroup_order': 360, 'subgroup_tex': 'C_{15}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '360.137', 'subgroup_hash': 137, 'subgroup_order': 360, 'subgroup_tex': 'D_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 120, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.128', 'subgroup_hash': 128, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 60, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.128', 'subgroup_hash': 128, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.127', 'subgroup_hash': 127, 'subgroup_order': 360, 'subgroup_tex': 'C_3:S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '360.129', 'subgroup_hash': 129, 'subgroup_order': 360, 'subgroup_tex': 'D_5.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 80, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '2880.hl.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.1595', 'subgroup_hash': 1595, 'subgroup_order': 320, 'subgroup_tex': 'D_{10}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 183536659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.919', 'subgroup_hash': 919, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.856', 'subgroup_hash': 856, 'subgroup_order': 288, 'subgroup_tex': 'D_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.897', 'subgroup_hash': 897, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.10.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.853', 'subgroup_hash': 853, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 183536714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.10.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.908', 'subgroup_hash': 908, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.10.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.854', 'subgroup_hash': 854, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 183536736
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 240, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.202', 'subgroup_hash': 202, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 240, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.194', 'subgroup_hash': 194, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 240, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.200', 'subgroup_hash': 200, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 240, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.201', 'subgroup_hash': 201, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 240, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.193', 'subgroup_hash': 193, 'subgroup_order': 240, 'subgroup_tex': 'A_4\\times F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 240, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.192', 'subgroup_hash': 192, 'subgroup_order': 240, 'subgroup_tex': 'A_4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '240.202', 'subgroup_hash': 202, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 120, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '240.135', 'subgroup_hash': 135, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536859
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '240.150', 'subgroup_hash': 150, 'subgroup_order': 240, 'subgroup_tex': 'D_6:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.137', 'subgroup_hash': 137, 'subgroup_order': 240, 'subgroup_tex': 'S_3\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.149', 'subgroup_hash': 149, 'subgroup_order': 240, 'subgroup_tex': 'D_6:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 60, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.200', 'subgroup_hash': 200, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.117', 'subgroup_hash': 117, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.201', 'subgroup_hash': 201, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.124', 'subgroup_hash': 124, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.136', 'subgroup_hash': 136, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.96', 'subgroup_hash': 96, 'subgroup_order': 240, 'subgroup_tex': 'D_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.96', 'subgroup_hash': 96, 'subgroup_order': 240, 'subgroup_tex': 'D_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183537003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183537014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.96', 'subgroup_hash': 96, 'subgroup_order': 240, 'subgroup_tex': 'D_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183537025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183537036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.96', 'subgroup_hash': 96, 'subgroup_order': 240, 'subgroup_tex': 'D_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183537042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 60, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.113', 'subgroup_hash': 113, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183537043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.95', 'subgroup_hash': 95, 'subgroup_order': 240, 'subgroup_tex': 'C_{15}:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183537044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.114', 'subgroup_hash': 114, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.120', 'subgroup_hash': 120, 'subgroup_order': 240, 'subgroup_tex': 'C_{60}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.121', 'subgroup_hash': 121, 'subgroup_order': 240, 'subgroup_tex': 'C_{60}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.97', 'subgroup_hash': 97, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.95', 'subgroup_hash': 95, 'subgroup_order': 240, 'subgroup_tex': 'C_{15}:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.97', 'subgroup_hash': 97, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.151', 'subgroup_hash': 151, 'subgroup_order': 240, 'subgroup_tex': 'D_6:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 30, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.138', 'subgroup_hash': 138, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.198', 'subgroup_hash': 198, 'subgroup_order': 240, 'subgroup_tex': 'A_4\\times D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 183536091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 120, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.196', 'subgroup_hash': 196, 'subgroup_order': 240, 'subgroup_tex': 'C_{10}\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.197', 'subgroup_hash': 197, 'subgroup_order': 240, 'subgroup_tex': 'C_{10}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 120, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.169', 'subgroup_hash': 169, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.150', 'subgroup_hash': 150, 'subgroup_order': 240, 'subgroup_tex': 'D_6:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 120, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.159', 'subgroup_hash': 159, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.149', 'subgroup_hash': 149, 'subgroup_order': 240, 'subgroup_tex': 'D_6:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.194', 'subgroup_hash': 194, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 40, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.194', 'subgroup_hash': 194, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 120, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.117', 'subgroup_hash': 117, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.124', 'subgroup_hash': 124, 'subgroup_order': 240, 'subgroup_tex': 'D_{10}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.193', 'subgroup_hash': 193, 'subgroup_order': 240, 'subgroup_tex': 'A_4\\times F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.192', 'subgroup_hash': 192, 'subgroup_order': 240, 'subgroup_tex': 'A_4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 80, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.193', 'subgroup_hash': 193, 'subgroup_order': 240, 'subgroup_tex': 'A_4\\times F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 40, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.192', 'subgroup_hash': 192, 'subgroup_order': 240, 'subgroup_tex': 'A_4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 183536107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.179', 'subgroup_hash': 179, 'subgroup_order': 240, 'subgroup_tex': 'D_4\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.194', 'subgroup_hash': 194, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.194', 'subgroup_hash': 194, 'subgroup_order': 240, 'subgroup_tex': 'D_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.151', 'subgroup_hash': 151, 'subgroup_order': 240, 'subgroup_tex': 'D_6:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 120, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.12.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.195', 'subgroup_hash': 195, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1469', 'subgroup_hash': 1469, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 183536118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.15.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1103', 'subgroup_hash': 1103, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 180, 'counter': 133, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '180.31', 'subgroup_hash': 31, 'subgroup_order': 180, 'subgroup_tex': 'A_4\\times C_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 183536120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 60, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 30, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 30, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 30, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 30, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 60, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 60, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 30, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 30, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.22', 'subgroup_hash': 22, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 30, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 30, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '180.30', 'subgroup_hash': 30, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.236', 'subgroup_hash': 236, 'subgroup_order': 160, 'subgroup_tex': 'C_2^3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.212', 'subgroup_hash': 212, 'subgroup_order': 160, 'subgroup_tex': 'C_2^3:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.203', 'subgroup_hash': 203, 'subgroup_order': 160, 'subgroup_tex': 'C_{10}:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.204', 'subgroup_hash': 204, 'subgroup_order': 160, 'subgroup_tex': 'D_{10}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.217', 'subgroup_hash': 217, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 80, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.236', 'subgroup_hash': 236, 'subgroup_order': 160, 'subgroup_tex': 'C_2^3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.212', 'subgroup_hash': 212, 'subgroup_order': 160, 'subgroup_tex': 'C_2^3:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 80, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 80, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': True, 'core_order': 144, 'counter': 160, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2880.hl.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 183536151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.155', 'subgroup_hash': 155, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 183536157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.20.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 120, 'counter': 172, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 120, 'counter': 173, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.44', 'subgroup_hash': 44, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 120, 'counter': 174, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 120, 'counter': 175, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.37', 'subgroup_hash': 37, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 120, 'counter': 176, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.46', 'subgroup_hash': 46, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 120, 'counter': 177, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.38', 'subgroup_hash': 38, 'subgroup_order': 120, 'subgroup_tex': 'C_5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': True, 'centralizer_order': 24, 'characteristic': True, 'core_order': 120, 'counter': 178, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2880.hl.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '120.9', 'subgroup_hash': 9, 'subgroup_order': 120, 'subgroup_tex': 'C_6.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.44', 'subgroup_hash': 44, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 60, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.17', 'subgroup_hash': 17, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.8', 'subgroup_hash': 8, 'subgroup_order': 120, 'subgroup_tex': 'C_6.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.46', 'subgroup_hash': 46, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.20', 'subgroup_hash': 20, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.30', 'subgroup_hash': 30, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 15, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.23', 'subgroup_hash': 23, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.11', 'subgroup_hash': 11, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.13', 'subgroup_hash': 13, 'subgroup_order': 120, 'subgroup_tex': 'C_5:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.27', 'subgroup_hash': 27, 'subgroup_order': 120, 'subgroup_tex': 'C_4\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.10', 'subgroup_hash': 10, 'subgroup_order': 120, 'subgroup_tex': 'D_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.11', 'subgroup_hash': 11, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.18', 'subgroup_hash': 18, 'subgroup_order': 120, 'subgroup_tex': 'C_3\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.12', 'subgroup_hash': 12, 'subgroup_order': 120, 'subgroup_tex': 'C_3:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.13', 'subgroup_hash': 13, 'subgroup_order': 120, 'subgroup_tex': 'C_5:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.12', 'subgroup_hash': 12, 'subgroup_order': 120, 'subgroup_tex': 'C_3:D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 15, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.28', 'subgroup_hash': 28, 'subgroup_order': 120, 'subgroup_tex': 'D_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 183536210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 60, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.43', 'subgroup_hash': 43, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 40, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 60, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.32', 'subgroup_hash': 32, 'subgroup_order': 120, 'subgroup_tex': 'D_4\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 60, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 60, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.37', 'subgroup_hash': 37, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 20, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.37', 'subgroup_hash': 37, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.20', 'subgroup_hash': 20, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.30', 'subgroup_hash': 30, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.38', 'subgroup_hash': 38, 'subgroup_order': 120, 'subgroup_tex': 'C_5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 20, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.38', 'subgroup_hash': 38, 'subgroup_order': 120, 'subgroup_tex': 'C_5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 20, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536228
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 60, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.41', 'subgroup_hash': 41, 'subgroup_order': 120, 'subgroup_tex': 'C_{30}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 20, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 60, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 20, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.24.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.78', 'subgroup_hash': 78, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.80', 'subgroup_hash': 80, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.100', 'subgroup_hash': 100, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536263
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 183536264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.30.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 30, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 30, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 15, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 30, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 15, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 15, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 80, 'counter': 284, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.51', 'subgroup_hash': 51, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 20, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '80.36', 'subgroup_hash': 36, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.44', 'subgroup_hash': 44, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.37', 'subgroup_hash': 37, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 20, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 20, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.30', 'subgroup_hash': 30, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.30', 'subgroup_hash': 30, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 10, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.30', 'subgroup_hash': 30, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.30', 'subgroup_hash': 30, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.51', 'subgroup_hash': 51, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.46', 'subgroup_hash': 46, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.44', 'subgroup_hash': 44, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 40, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 40, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 40, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.36.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 72, 'counter': 331, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 72, 'counter': 332, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 72, 'counter': 333, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.40.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '2880.hl.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 183536355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 60, 'counter': 346, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.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': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 60, 'counter': 347, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.9', 'subgroup_hash': 9, 'subgroup_order': 60, 'subgroup_tex': 'C_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 60, 'counter': 348, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536358
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 60, 'counter': 349, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536360
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 60, 'counter': 350, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 30, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 30, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 30, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 15, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 15, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536372
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 361, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 183536373
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536374
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 15, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536375
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 20, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.9', 'subgroup_hash': 9, 'subgroup_order': 60, 'subgroup_tex': 'C_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 30, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 30, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536386
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 30, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 10, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536390
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 30, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536391
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 30, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536393
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 30, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536394
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536395
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 20, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536396
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536397
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536398
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536399
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 20, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536400
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 10, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 15, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 30, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 30, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536413
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 15, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536416
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.48.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 183536430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': 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: 183536431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536433
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536434
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536440
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536442
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': 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: 183536447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': 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: 183536449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': 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: 183536451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': 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: 183536467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': 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: 183536468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536471
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536474
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536485
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.60.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 15, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 15, 'label': '2880.hl.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 40, 'counter': 465, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536488
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536491
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536494
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 20, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536500
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536502
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536505
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 5, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 5, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 5, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 20, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 20, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 20, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 20, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 20, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.72.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 36, 'counter': 529, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': 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: 183536567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': 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: 183536568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': 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: 183536569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.80.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.90.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.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': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536588
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 30, 'counter': 556, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536589
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 30, 'counter': 557, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536590
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 30, 'counter': 558, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536591
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 15, 'counter': 559, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 560, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536594
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 10, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536595
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 10, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536596
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 15, 'counter': 563, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 183536597
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536598
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 15, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536599
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536600
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 15, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536601
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 15, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536602
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 5, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536604
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536605
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 15, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536606
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536607
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 15, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536608
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 15, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536609
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 5, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536610
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 5, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 24, 'counter': 577, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': True, 'centralizer_order': 120, 'characteristic': True, 'core_order': 24, 'counter': 578, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2880.hl.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, '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: 183536621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536622
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, '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: 183536624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, '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: 183536626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, '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: 183536627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, '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: 183536628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, '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: 183536629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 3, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 3, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 183536654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 12, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 12, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 12, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 12, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536678
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536679
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536683
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, '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: 183536686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.120.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 20, 'counter': 659, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.143', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 143, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536704
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': True, 'centralizer_order': 144, 'characteristic': True, 'core_order': 20, 'counter': 660, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2880.hl.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 5, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 10, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 5, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 5, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536712
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 5, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536716
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 671, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536717
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 672, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 183536718
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 5, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536719
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 10, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 5, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536726
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536728
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 10, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536729
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 10, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536730
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 10, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536731
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 10, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536732
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 10, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536735
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 5, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536737
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 5, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536743
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 5, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536744
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.144.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536749
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': 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: 183536750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.160.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.160.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.160.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 183536756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': 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: 183536773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536777
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 183536791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536796
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536805
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536806
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.180.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': 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: 183536807
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': True, 'core_order': 15, 'counter': 753, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2880.hl.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1469', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1469, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536808
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 754, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536809
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 5, 'counter': 755, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 183536810
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 12, 'counter': 756, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.195', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 195, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times F_5', '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: 183536811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 12, 'counter': 757, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.195', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 195, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 6, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 3, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 3, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 768, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536824
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 3, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536826
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 770, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536827
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': 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: 183536828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 4, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 183536829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536843
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 786, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536844
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 787, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536845
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536846
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 789, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536848
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536849
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536850
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 792, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536851
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 793, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536852
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536853
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536854
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 796, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536855
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 3, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536861
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536862
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536869
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 809, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.240.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536871
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': 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: 183536872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.240.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 183536873
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 10, 'counter': 812, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536874
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 5, 'counter': 813, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536875
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 5, 'counter': 814, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 5, 'counter': 815, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536877
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 5, 'counter': 816, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.288.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536878
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 5, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.288.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536879
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 5, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.288.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536880
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 5, 'counter': 819, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.288.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 183536882
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 5, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.288.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536883
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 5, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.288.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536884
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 5, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.288.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 183536885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '2880.hl.320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 183536886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536887
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536888
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536894
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536895
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536896
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536897
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536898
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536900
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536901
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': 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: 183536904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536905
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536906
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 4, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 183536933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536953
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 183536955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.360.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': 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: 183536956
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': True, 'centralizer_order': 480, 'characteristic': True, 'core_order': 6, 'counter': 888, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2880.hl.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.1189', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1189, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_5\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536957
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 3, 'counter': 889, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536959
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 890, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536960
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 891, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536961
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 892, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536962
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 893, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536963
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 894, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536964
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536965
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 3, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536966
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 897, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536967
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536968
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 899, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536971
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 3, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536972
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536973
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 903, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.480.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, 'quotient_simple': 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: 183536975
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536976
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536977
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536978
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536979
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.480.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 183536980
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': True, 'core_order': 5, 'counter': 909, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '2880.hl.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.8311', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8311, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times S_3\\times S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 183536982
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 4, 'counter': 910, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2880.hl.720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '720.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '720.783', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 783, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 720, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 183536983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 1, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536984
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536987
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536989
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536990
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 921, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 922, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 923, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 924, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': 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: 183536999
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537001
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537002
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537005
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 932, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 933, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537008
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 934, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537009
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 935, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537010
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 936, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537011
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 937, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537018
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537020
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537021
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537022
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 947, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537023
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 948, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2880.hl.720.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': 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: 183537026
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': True, 'core_order': 3, 'counter': 950, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2880.hl.960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '960.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '960.11361', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11361, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 960, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times F_5\\times S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 183537027
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 951, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.960.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.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': 960, '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: 183537028
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 952, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.960.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.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': 960, '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: 183537029
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 1, 'counter': 953, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537030
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 1, 'counter': 954, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537031
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 955, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537032
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 956, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537033
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 1, 'counter': 957, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537034
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 958, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537035
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 959, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537037
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 960, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 961, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537039
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 962, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537040
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 963, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2880.hl.1440.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, '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: 183537041
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2880.hl', 'ambient_counter': 194, 'ambient_order': 2880, 'ambient_tex': 'S_3\\times F_5\\times S_4', 'central': True, 'central_factor': False, 'centralizer_order': 2880, 'characteristic': True, 'core_order': 1, 'counter': 964, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '2880.hl.2880.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2880.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '2880.hl', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 799193401477229059, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2880, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times F_5\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D3', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 183536081
    {'ambient': '2880.hl', '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': '2880.a1.a1', 'complements': ['2880.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '3.b1.a1', '4.l1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5841, 3499, 5878, 3794, 5391, 5655, 2292, 4345], 'generators': [11, 124, 23, 3669967, 1456, 5, 8025137, 50803200, 7], 'label': '2880.hl.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '2880.hl', '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': '2880.hl'}
  • id: 183536082
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.n1.a1', '6.o1.a1', '6.p1.a1', '6.q1.a1', '6.s1.a1', '6.t1.a1', '9.a1.a1', '15.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7768, -1, 7810, -1, 7216, -1, 6389, -1], 'generators': [127, 23, 3669967, 1456, 5, 8025134, 50803200, 7], 'label': '2880.hl.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536083
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.j1.a1', '6.q1.a1'], 'contains': ['24.r1.a1', '24.t1.a1', '24.z1.a1', '36.ba1.a1', '60.z1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7937, -1, 7053, -1, 7016, -1, 7356, -1], 'generators': [3669960, 1456, 8025258, 9, 50803200, 16], 'label': '2880.hl.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536084
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.i1.a1', '6.q1.a1'], 'contains': ['24.r1.a1', '24.x1.a1', '24.y1.a1', '36.bb1.a1', '60.ba1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8651, -1, 9154, -1, 7922, -1, 7318, -1], 'generators': [3669960, 1456, 8025254, 9, 50803200, 16], 'label': '2880.hl.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536085
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.h1.a1', '6.s1.a1'], 'contains': ['24.s1.a1', '24.u1.a1', '24.y1.a1', '36.bc1.a1', '60.bb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8624, -1, 8837, -1, 7205, -1, 7284, -1], 'generators': [23, 3669960, 8025136, 1463, 8025261, 50803200], 'label': '2880.hl.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536086
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.h1.a1', '6.t1.a1'], 'contains': ['24.t1.a1', '24.u1.a1', '24.v1.a1', '36.bd1.a1', '60.bc1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7048, -1, 7981, -1, 6972, -1, 7470, -1], 'generators': [23, 3669960, 130, 1463, 8025133, 50803200], 'label': '2880.hl.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536087
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.g1.a1', '6.t1.a1'], 'contains': ['24.u1.a1', '24.w1.a1', '24.x1.a1', '36.be1.a1', '60.bd1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9033, -1, 9536, -1, 8006, -1, 7083, -1], 'generators': [23, 3669960, 130, 1463, 8025141, 50803200], 'label': '2880.hl.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536088
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1'], 'contains': ['24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.be1.a1', '24.bh1.a1', '24.bk1.a1', '24.bn1.a1', '36.bf1.a1', '60.be1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3450, -1, 3634, -1, 3154, -1, 3812, -1], 'generators': [127, 3669967, 1456, 5, 50803200, 16], 'label': '2880.hl.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536089
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1'], 'contains': ['24.be1.a1', '24.bf1.a1', '24.bg1.a1', '24.bi1.a1', '24.bj1.a1', '24.bl1.a1', '24.bm1.a1', '36.bg1.a1', '60.bf1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2627, -1, 2559, -1, 3098, -1, 4221, -1], 'generators': [127, 3669967, 1456, 9, 50803200, 16], 'label': '2880.hl.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536090
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.c1.a1', '24.br1.a1', '24.bu1.a1', '36.bh1.a1', '48.u1.a1', '60.bg1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2444, -1, 1916, -1, 1205, -1, 2032, -1], 'generators': [11, 124, 23, 3669143, 50803200, 7], 'label': '2880.hl.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536091
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.br1.a1', '24.bw1.a1', '36.bi1.a1', '48.v1.a1', '60.bh1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1380, -1, 1092, -1, 830, -1, 898, -1], 'generators': [11, 124, 23, 5, 50803200, 7], 'label': '2880.hl.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 183536092
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.k1.a1'], 'contains': ['24.f1.a1', '24.br1.a1', '24.ca1.a1', '36.bj1.a1', '48.w1.a1', '60.bi1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1486, -1, 1128, -1, 954, -1, 854, -1], 'generators': [11, 7, 23, 124, 3669138, 50803200], 'label': '2880.hl.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536093
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.d1.a1', '12.a1.a1', '12.bm1.a1', '16.b1.a1', '20.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2664, 4691, 2042, 3794, 1266, 5702, 1838, 4298], 'generators': [11, 124, 23, 3669967, 1456, 50803200, 7], 'label': '2880.hl.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.d1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536094
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.206', 'aut_weyl_index': 30, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.n1.a1'], 'contains': ['24.a1.a1', '24.i1.a1', '24.l1.a1', '24.ba1.a1', '24.bf1.a1', '24.bt1.a1', '24.bv1.a1', '36.bi1.a1', '60.bk1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2014, -1, 1450, -1, 2352, -1, 3180, -1], 'generators': [127, 23, 1456, 5, 50803200, 7], 'label': '2880.hl.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 183536095
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.n1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '24.m1.a1', '24.bg1.a1', '24.bh1.a1', '24.by1.a1', '24.bz1.a1', '36.bj1.a1', '60.bl1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2355, -1, 2004, -1, 2402, -1, 3130, -1], 'generators': [127, 23, 1456, 3669969, 50803200, 7], 'label': '2880.hl.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536096
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.n1.a1', '6.p1.a1', '6.q1.a1'], 'contains': ['24.b1.a1', '24.n1.a1', '24.r1.a1', '24.bc1.a1', '24.bm1.a1', '24.bt1.a1', '24.by1.a1', '36.bk1.a1', '60.bm1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3315, -1, 1673, -1, 3463, -1, 3966, -1], 'generators': [23, 3669967, 1456, 5, 50803200, 7], 'label': '2880.hl.12.br1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}
  • id: 183536097
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.n1.a1', '6.s1.a1', '6.t1.a1'], 'contains': ['24.b1.a1', '24.p1.a1', '24.u1.a1', '24.bl1.a1', '24.bn1.a1', '24.bv1.a1', '24.bz1.a1', '36.bl1.a1', '60.bo1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2286, -1, 2335, -1, 2936, -1, 3915, -1], 'generators': [23, 3669967, 122, 1456, 50803200, 7], 'label': '2880.hl.12.bs1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536098
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.k1.a1', '6.u1.a1', '6.v1.a1'], 'contains': ['24.c1.a1', '24.bw1.a1', '24.ca1.a1', '36.bl1.a1', '48.be1.a1', '60.bp1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1785, -1, 1878, -1, 1444, -1, 1306, -1], 'generators': [11, 23, 122, 3669143, 50803200, 7], 'label': '2880.hl.12.bt1.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.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536099
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.w1.a1'], 'contains': ['24.bs1.a1', '24.bx1.a1', '24.cb1.a1', '36.bl1.a1', '48.bf1.a1', '60.bq1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1813, -1, 1970, -1, 1998, -1, 1352, -1], 'generators': [23, 122, 1460, 3669964, 50803200, 7], 'label': '2880.hl.12.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536100
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.o1.a1', '6.p1.a1', '6.t1.a1'], 'contains': ['24.b1.a1', '24.v1.a1', '24.w1.a1', '36.bn1.a1', '60.bt1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6899, -1, 7111, -1, 6305, -1, 5833, -1], 'generators': [23, 3669967, 1456, 8025137, 50803200, 7], 'label': '2880.hl.12.bv1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}
  • id: 183536101
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.o1.a1', '6.q1.a1', '6.s1.a1'], 'contains': ['24.b1.a1', '24.y1.a1', '24.z1.a1', '36.bo1.a1', '60.bu1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7108, -1, 6900, -1, 6025, -1, 6264, -1], 'generators': [23, 3669967, 1456, 8025253, 50803200, 7], 'label': '2880.hl.12.bw1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536102
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.l1.a1', '6.r1.a1', '6.v1.a1'], 'contains': ['24.c1.a1', '36.bm1.a1', '48.bl1.a1', '60.bw1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5385, -1, 5475, -1, 5064, -1, 2664, -1], 'generators': [11, 23, 8025255, 3669143, 50803200, 7], 'label': '2880.hl.12.bx1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536103
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.m1.a1', '6.r1.a1', '6.u1.a1'], 'contains': ['24.c1.a1', '36.bo1.a1', '48.bn1.a1', '60.by1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6105, -1, 6195, -1, 4875, -1, 2523, -1], 'generators': [11, 23, 8025253, 3669143, 50803200, 7], 'label': '2880.hl.12.by1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536104
    {'ambient': '2880.hl', 'aut_centralizer_order': 5, 'aut_label': '4.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '576.8311', 'aut_weyl_index': 5, 'centralizer': '576.a1.a1', 'complements': ['720.bl1.a1', '720.z1.a1', '720.bb1.a1', '720.bm1.a1', '720.w1.a1', '720.x1.a1', '720.y1.a1', '720.ba1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.e1.a1', '12.bn1.a1', '12.bp1.a1', '16.c1.a1', '20.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1376, 9524, 996, 9551, 1050, 374, 735, 9626], 'generators': [11, 124, 23, 1456, 5, 50803200, 7], 'label': '2880.hl.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.e1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8311'}
  • id: 183536105
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.w1.a1'], 'contains': ['24.bs1.a1', '36.a1.a1', '48.bo1.a1', '60.bz1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5262, -1, 5348, -1, 5840, -1, 2247, -1], 'generators': [23, 8025132, 1460, 3669964, 50803200, 7], 'label': '2880.hl.12.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '12.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536106
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.w1.a1'], 'contains': ['24.bs1.a1', '36.bo1.a1', '48.bp1.a1', '60.ca1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6184, -1, 6256, -1, 5917, -1, 2287, -1], 'generators': [23, 1460, 3669964, 8025253, 50803200, 7], 'label': '2880.hl.12.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536107
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.n1.a1'], 'contains': ['24.e1.a1', '24.bb1.a1', '24.bd1.a1', '24.bj1.a1', '24.bq1.a1', '24.bt1.a1', '24.bz1.a1', '36.bp1.a1', '60.cb1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1891, -1, 3216, -1, 2038, -1, 2990, -1], 'generators': [23, 1456, 5, 3669863, 50803200, 7], 'label': '2880.hl.12.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536108
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.bu1.a1', '24.ca1.a1', '36.bp1.a1', '48.bu1.a1', '60.cc1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1453, -1, 1256, -1, 1039, -1, 741, -1], 'generators': [11, 23, 5, 3669848, 50803200, 7], 'label': '2880.hl.12.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536109
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.k1.a1'], 'contains': ['24.f1.a1', '24.bu1.a1', '24.bw1.a1', '36.bq1.a1', '48.by1.a1', '60.cd1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1560, -1, 1342, -1, 869, -1, 814, -1], 'generators': [11, 7, 23, 3669138, 3669848, 50803200], 'label': '2880.hl.12.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536110
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.n1.a1'], 'contains': ['24.e1.a1', '24.bi1.a1', '24.bk1.a1', '24.bo1.a1', '24.bp1.a1', '24.bv1.a1', '24.by1.a1', '36.bq1.a1', '60.ce1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2316, -1, 1762, -1, 2076, -1, 3029, -1], 'generators': [23, 1456, 3669863, 3669969, 50803200, 7], 'label': '2880.hl.12.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ce1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536111
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.l1.a1'], 'contains': ['24.cc1.a1', '24.cd1.a1', '24.ce1.a1', '24.cp1.a1', '24.cq1.a1', '24.cz1.a1', '24.da1.a1', '36.br1.a1', '60.cf1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5684, -1, 5845, -1, 4961, -1, 2428, -1], 'generators': [8023681, 124, 5, 3669120, 3, 50803200], 'label': '2880.hl.12.cf1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '12.cf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536112
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.c1.a1'], 'contains': ['24.g1.a1', '24.cf1.a1', '24.ch1.a1', '24.cl1.a1', '24.cn1.a1', '24.cv1.a1', '24.cx1.a1', '36.br1.a1', '60.cg1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8264, -1, 8289, -1, 6133, -1, 8982, -1], 'generators': [1440, 3669960, 5, 8025125, 120, 50803200], 'label': '2880.hl.12.cg1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.cg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536113
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.cf1.a1', '24.cg1.a1', '24.ch1.a1', '24.cm1.a1', '24.co1.a1', '24.cw1.a1', '24.cy1.a1', '36.bs1.a1', '60.ch1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9349, -1, 9111, -1, 7441, -1, 9333, -1], 'generators': [1440, 3669960, 5, 8025134, 120, 50803200], 'label': '2880.hl.12.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.ch1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536114
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.ck1.a1', '24.cl1.a1', '24.co1.a1', '24.cr1.a1', '24.cu1.a1', '24.cv1.a1', '24.cy1.a1', '36.bt1.a1', '60.ci1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8538, -1, 8505, -1, 6780, -1, 9106, -1], 'generators': [136, 1440, 3669960, 5, 8025125, 50803200], 'label': '2880.hl.12.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.ci1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536115
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['720.bl1.a1', '720.z1.a1', '720.bm1.a1', '720.bb1.a1', '720.w1.a1', '720.x1.a1', '720.y1.a1', '720.ba1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '12.bo1.a1', '12.bq1.a1', '16.d1.a1', '20.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1480, 7964, 1203, 7990, 1102, 1818, 684, 8182], 'generators': [11, 124, 23, 1456, 3669969, 50803200, 7], 'label': '2880.hl.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.f1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536116
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.ck1.a1', '24.cm1.a1', '24.cn1.a1', '24.cs1.a1', '24.cu1.a1', '24.cw1.a1', '24.cx1.a1', '36.bu1.a1', '60.cj1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9200, -1, 8706, -1, 7067, -1, 9177, -1], 'generators': [136, 1440, 3669960, 5, 8025134, 50803200], 'label': '2880.hl.12.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.cj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536117
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.i1.a1', '30.j1.a1', '30.k1.a1', '30.q1.a1', '30.r1.a1', '30.u1.a1', '30.v1.a1', '45.a1.a1', '60.cf1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5816, -1, 5944, -1, 4995, -1, 1671, -1], 'generators': [11, 124, 23, 8023697, 5, 3669143, 7], 'label': '2880.hl.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536118
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '15.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1', '30.d1.a1', '30.e1.a1', '30.f1.a1', '30.g1.a1', '30.h1.a1', '30.l1.a1', '30.m1.a1', '30.n1.a1', '30.o1.a1', '30.p1.a1', '30.s1.a1', '30.t1.a1', '45.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7576, -1, 7684, -1, 8468, -1, 5748, -1], 'generators': [127, 23, 3669967, 1456, 5, 8025134, 7], 'label': '2880.hl.15.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '15.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536119
    {'ambient': '2880.hl', 'aut_centralizer_order': 15, 'aut_label': '16.a1', 'aut_quo_index': 192, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 15, 'centralizer': '192.a1.a1', 'complements': ['180.bt1.a1', '180.bu1.a1', '180.bs1.a1', '180.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.t1.a1', '64.a1.a1', '80.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1262, 6523, 974, 6536, 750, 3490, 340, 6495], 'generators': [11, 23, 1456, 50803200, 7], 'label': '2880.hl.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '16.10', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1469'}
  • id: 183536120
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.d1.a1', '48.c1.a1', '48.u1.a1', '80.b1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2921, -1, 2407, -1, 988, -1, 2090, -1], 'generators': [124, 1440, 3669960, 3, 50803200], 'label': '2880.hl.16.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536121
    {'ambient': '2880.hl', 'aut_centralizer_order': 5, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.143', 'aut_weyl_index': 20, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.e1.a1', '48.v1.a1', '48.x1.a1', '80.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2969, -1, 2791, -1, 1518, -1, 499, -1], 'generators': [124, 1440, 5, 3, 50803200], 'label': '2880.hl.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 183536122
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.g1.a1', '48.w1.a1', '48.z1.a1', '80.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2768, -1, 2141, -1, 1093, -1, 446, -1], 'generators': [1440, 128, 3669974, 12, 50803200], 'label': '2880.hl.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.d1.a1', 'projective_image': '2880.hl', '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': '720.783'}
  • id: 183536123
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '8.h1.a1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.f1.a1', '48.ba1.a1', '48.bb1.a1', '80.e1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3405, -1, 3588, -1, 2258, -1, 1090, -1], 'generators': [11, 1440, 3669960, 5, 50803200], 'label': '2880.hl.16.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536124
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '8.h1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.g1.a1', '48.bd1.a1', '48.be1.a1', '48.bf1.a1', '80.f1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3192, -1, 3397, -1, 2974, -1, 1343, -1], 'generators': [1440, 3669960, 122, 12, 50803200], 'label': '2880.hl.16.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536125
    {'ambient': '2880.hl', 'aut_centralizer_order': 9, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '8.i1.a1', '8.k1.a1', '8.m1.a1'], 'contains': ['32.b1.a1', '48.d1.a1', '48.bk1.a1', '48.bo1.a1', '80.g1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5233, -1, 5355, -1, 5676, -1, 2332, -1], 'generators': [1440, 8025132, 3669960, 12, 50803200], 'label': '2880.hl.16.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536126
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 3, 'centralizer': '960.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.f1.a1', '12.b1.a1', '12.br1.a1', '16.e1.a1', '20.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3324, 5596, 1825, 5621, 2278, 4011, 1125, 5989], 'generators': [11, 23, 3669967, 1456, 5, 50803200, 7], 'label': '2880.hl.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.f1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '2880.hl', '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': '960.11361'}
  • id: 183536127
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '8.i1.a1', '8.l1.a1', '8.n1.a1'], 'contains': ['32.b1.a1', '48.e1.a1', '48.bl1.a1', '80.h1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5404, -1, 5525, -1, 5171, -1, 2488, -1], 'generators': [1440, 3669960, 8025255, 20, 50803200], 'label': '2880.hl.16.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536128
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '8.j1.a1', '8.k1.a1', '8.n1.a1'], 'contains': ['32.b1.a1', '48.bh1.a1', '48.bm1.a1', '80.i1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6336, -1, 6390, -1, 5469, -1, 2186, -1], 'generators': [11, 1440, 3669960, 8025126, 50803200], 'label': '2880.hl.16.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536129
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '8.j1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.b1.a1', '48.bj1.a1', '48.bn1.a1', '48.bp1.a1', '80.j1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6130, -1, 6231, -1, 5757, -1, 2414, -1], 'generators': [11, 1440, 3669960, 8025261, 50803200], 'label': '2880.hl.16.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536130
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '8.h1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.g1.a1', '48.br1.a1', '48.bu1.a1', '80.k1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2872, -1, 2585, -1, 1219, -1, 123, -1], 'generators': [1440, 5, 3669844, 3, 50803200], 'label': '2880.hl.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536131
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '8.h1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.f1.a1', '48.by1.a1', '48.bz1.a1', '80.l1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2718, -1, 2180, -1, 1161, -1, 242, -1], 'generators': [1440, 3669974, 12, 3669848, 50803200], 'label': '2880.hl.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536132
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.g1.a1', '36.k1.a1', '36.m1.a1', '36.t1.a1', '36.v1.a1', '36.br1.a1', '36.bs1.a1', '36.bt1.a1', '36.bu1.a1', '90.a1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8720, -1, 8664, -1, 6879, -1, 8035, -1], 'generators': [8023694, 5, 3669136, 120, 50803200, 16], 'label': '2880.hl.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536133
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.e1.a1', '36.f1.a1', '36.l1.a1', '36.n1.a1', '36.u1.a1', '36.w1.a1', '90.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7006, -1, 6891, -1, 7575, -1, 7715, -1], 'generators': [5, 8023698, 3669136, 120, 50803200, 16], 'label': '2880.hl.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '2880.hl', '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': '80.50'}
  • id: 183536134
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.d1.a1', '36.f1.a1', '36.x1.a1', '36.y1.a1', '36.ba1.a1', '36.bd1.a1', '90.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7365, -1, 7427, -1, 6538, -1, 7165, -1], 'generators': [8023698, 9, 3669136, 120, 50803200, 16], 'label': '2880.hl.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536135
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.g1.a1', '36.z1.a1', '36.bb1.a1', '36.bc1.a1', '36.be1.a1', '90.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9119, -1, 9232, -1, 7884, -1, 6962, -1], 'generators': [8023694, 9, 3669136, 120, 50803200, 16], 'label': '2880.hl.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '2880.hl', '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': '80.50'}
  • id: 183536136
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.j1.a1', '36.k1.a1', '36.n1.a1', '36.p1.a1', '36.s1.a1', '36.y1.a1', '36.be1.a1', '90.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7835, -1, 7576, -1, 7395, -1, 7119, -1], 'generators': [127, 8023694, 5, 3669136, 50803200, 16], 'label': '2880.hl.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '2880.hl', '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': '80.50'}
  • id: 183536137
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.g1.a1', '12.bs1.a1', '12.bt1.a1', '12.bu1.a1', '16.f1.a1', '20.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2174, 6408, 2140, 6434, 1998, 3259, 1329, 6741], 'generators': [11, 23, 3669967, 122, 1456, 50803200, 7], 'label': '2880.hl.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '2880.hl', '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': '2880.hl'}
  • id: 183536138
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.a1.a1'], 'contains': ['36.j1.a1', '36.l1.a1', '36.m1.a1', '36.q1.a1', '36.r1.a1', '36.bc1.a1', '36.bd1.a1', '90.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7450, -1, 7903, -1, 7113, -1, 7212, -1], 'generators': [127, 5, 8023698, 3669136, 50803200, 16], 'label': '2880.hl.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536139
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.a1.a1'], 'contains': ['36.o1.a1', '36.p1.a1', '36.r1.a1', '36.t1.a1', '36.w1.a1', '36.x1.a1', '36.bb1.a1', '90.g1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7613, -1, 8069, -1, 7241, -1, 7248, -1], 'generators': [127, 8023698, 9, 3669136, 50803200, 16], 'label': '2880.hl.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536140
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '9.a1.a1'], 'contains': ['36.o1.a1', '36.q1.a1', '36.s1.a1', '36.u1.a1', '36.v1.a1', '36.z1.a1', '36.ba1.a1', '90.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8111, -1, 7521, -1, 7334, -1, 7002, -1], 'generators': [127, 8023694, 9, 3669136, 50803200, 16], 'label': '2880.hl.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536141
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '6.n1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.d1.a1', '36.h1.a1', '36.i1.a1', '36.j1.a1', '36.o1.a1', '36.bf1.a1', '36.bg1.a1', '36.bh1.a1', '36.bi1.a1', '36.bj1.a1', '36.bk1.a1', '36.bl1.a1', '36.bp1.a1', '36.bq1.a1', '90.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2326, -1, 2348, -1, 2530, -1, 4023, -1], 'generators': [127, 23, 5, 3669143, 50803200, 7], 'label': '2880.hl.18.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536142
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.l1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.c1.a1', '36.e1.a1', '36.p1.a1', '36.q1.a1', '36.bh1.a1', '36.bm1.a1', '90.j1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8522, -1, 9005, -1, 7657, -1, 6403, -1], 'generators': [127, 23, 3669143, 8023696, 50803200, 7], 'label': '2880.hl.18.j1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536143
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '6.o1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.g1.a1', '36.r1.a1', '36.s1.a1', '36.bh1.a1', '36.bn1.a1', '36.bo1.a1', '90.k1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7128, -1, 6932, -1, 6186, -1, 6357, -1], 'generators': [127, 23, 8023697, 3669143, 50803200, 7], 'label': '2880.hl.18.k1.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.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536144
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.p1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.k1.a1', '36.l1.a1', '36.x1.a1', '36.z1.a1', '36.bk1.a1', '36.bn1.a1', '90.l1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 7857, -1, 6621, -1, 5716, -1], 'generators': [23, 8023694, 5, 3669143, 50803200, 7], 'label': '2880.hl.18.l1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536145
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '6.r1.a1', '9.a1.a1'], 'contains': ['36.m1.a1', '36.n1.a1', '36.ba1.a1', '36.bb1.a1', '36.bk1.a1', '36.bm1.a1', '36.bo1.a1', '90.m1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7946, -1, 7246, -1, 7487, -1, 6222, -1], 'generators': [23, 5, 8025254, 3669143, 50803200, 7], 'label': '2880.hl.18.m1.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.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536146
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1', '6.u1.a1', '6.w1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.t1.a1', '36.u1.a1', '36.y1.a1', '36.bc1.a1', '36.bl1.a1', '36.bo1.a1', '90.n1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7754, -1, 7216, -1, 6585, -1, 5789, -1], 'generators': [8025253, 8023696, 23, 7, 3669143, 50803200], 'label': '2880.hl.18.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536147
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.v1.a1', '9.a1.a1'], 'contains': ['36.v1.a1', '36.w1.a1', '36.bd1.a1', '36.be1.a1', '36.bl1.a1', '36.bm1.a1', '36.bn1.a1', '90.o1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7070, -1, 7940, -1, 7618, -1, 5753, -1], 'generators': [23, 122, 8023693, 3669143, 50803200, 7], 'label': '2880.hl.18.o1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536148
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 3, 'centralizer': '960.a1.a1', 'complements': ['720.bc1.a1', '720.q1.a1', '720.bi1.a1', '720.s1.a1', '720.bn1.a1', '720.bj1.a1', '720.bf1.a1', '720.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '12.c1.a1', '12.e1.a1', '12.bz1.a1', '16.g1.a1', '20.f1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5174, 894, 5227, 922, 5658, 8740, 2259, 1261], 'generators': [11, 23, 8025132, 3669967, 1456, 50803200, 7], 'label': '2880.hl.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.c1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '960.11361'}
  • id: 183536149
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '144.b1.a1', 'complements': ['144.bl1.a1', '144.z1.a1', '144.bm1.a1', '144.bb1.a1', '144.b1.a1', '144.x1.a1', '144.y1.a1', '144.ba1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.c1.a1', '60.bh1.a1', '60.bk1.a1', '80.c1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [415, 8320, 253, 8262, 692, 550, 453, 9450], 'generators': [11, 124, 23, 1456, 5, 7], 'label': '2880.hl.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['40.a1.a1', '40.b1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536150
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '40.d1.a1', '40.e1.a1', '60.bg1.a1', '60.bj1.a1', '80.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [845, -1, 713, -1, 574, -1, 1219, -1], 'generators': [11, 124, 23, 3669967, 1456, 7], 'label': '2880.hl.20.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536151
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.f1.a1', '40.g1.a1', '60.bi1.a1', '60.bl1.a1', '80.d1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [584, -1, 453, -1, 528, -1, 417, -1], 'generators': [11, 124, 23, 1456, 3669969, 7], 'label': '2880.hl.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536152
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.a1.a1', '10.d1.a1', '10.e1.a1'], 'contains': ['40.b1.a1', '40.d1.a1', '40.f1.a1', '60.bm1.a1', '60.bn1.a1', '80.e1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3274, -1, 1204, -1, 2289, -1, 777, -1], 'generators': [11, 23, 3669967, 1456, 5, 7], 'label': '2880.hl.20.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536153
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.a1.a1', '10.f1.a1', '10.g1.a1'], 'contains': ['40.c1.a1', '40.d1.a1', '40.g1.a1', '60.bo1.a1', '60.bp1.a1', '60.bq1.a1', '80.f1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1138, -1, 1689, -1, 1958, -1, 1051, -1], 'generators': [11, 23, 3669967, 122, 1456, 7], 'label': '2880.hl.20.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536154
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '10.b1.a1', '10.d1.a1', '10.f1.a1'], 'contains': ['40.d1.a1', '60.br1.a1', '60.bv1.a1', '60.bz1.a1', '80.g1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5295, -1, 5326, -1, 5679, -1, 1822, -1], 'generators': [11, 23, 8025132, 3669967, 1456, 7], 'label': '2880.hl.20.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536155
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '10.b1.a1', '10.e1.a1', '10.g1.a1'], 'contains': ['40.d1.a1', '60.bs1.a1', '60.bw1.a1', '80.h1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5434, -1, 5495, -1, 5114, -1, 1531, -1], 'generators': [11, 23, 3669967, 1456, 8025255, 7], 'label': '2880.hl.20.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536156
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '10.c1.a1', '10.d1.a1', '10.g1.a1'], 'contains': ['40.d1.a1', '60.bt1.a1', '60.bx1.a1', '80.i1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6295, -1, 6313, -1, 5514, -1, 1403, -1], 'generators': [11, 23, 3669967, 1456, 8025137, 7], 'label': '2880.hl.20.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536157
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.i1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '10.c1.a1', '10.e1.a1', '10.f1.a1'], 'contains': ['40.d1.a1', '60.bu1.a1', '60.by1.a1', '60.ca1.a1', '80.j1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6137, -1, 6207, -1, 5788, -1, 1777, -1], 'generators': [11, 23, 3669967, 1456, 8025253, 7], 'label': '2880.hl.20.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536158
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.j1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '10.a1.a1'], 'contains': ['40.b1.a1', '40.e1.a1', '40.g1.a1', '60.cb1.a1', '60.cc1.a1', '80.k1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [379, -1, 581, -1, 620, -1, 188, -1], 'generators': [11, 23, 1456, 5, 3669848, 7], 'label': '2880.hl.20.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536159
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['720.bc1.a1', '720.q1.a1', '720.bf1.a1', '720.bd1.a1', '720.bi1.a1', '720.s1.a1', '720.bn1.a1', '720.bj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.d1.a1', '12.bx1.a1', '16.h1.a1', '20.g1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5413, 1922, 5497, 1950, 5098, 7937, 2492, 2063], 'generators': [11, 23, 3669967, 1456, 8025255, 50803200, 7], 'label': '2880.hl.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536160
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.k1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '10.a1.a1'], 'contains': ['40.c1.a1', '40.e1.a1', '40.f1.a1', '60.cd1.a1', '60.ce1.a1', '80.l1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [520, -1, 334, -1, 656, -1, 301, -1], 'generators': [11, 23, 1456, 3669969, 3669848, 7], 'label': '2880.hl.20.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.k1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536161
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '20.l1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '5.a1.a1'], 'contains': ['40.h1.a1', '40.i1.a1', '40.j1.a1', '40.k1.a1', '40.l1.a1', '40.m1.a1', '40.n1.a1', '60.cf1.a1', '60.cg1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5861, -1, 5916, -1, 5460, -1, 1584, -1], 'generators': [124, 1440, 3669960, 5, 8025121, 3], 'label': '2880.hl.20.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '20.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536162
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '24.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '144.143', 'aut_weyl_index': 20, 'centralizer': '144.a1.a1', 'complements': ['120.cp1.a1', '120.cq1.a1', '120.cz1.a1', '120.db1.a1', '120.da1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.bp1.a1', '12.bq1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.i1.a1', '72.bl1.a1', '120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3155, 5215, 2276, 4543, 2687, 4629, 3078, 5355], 'generators': [127, 23, 1456, 50803200, 7], 'label': '2880.hl.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '96.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '24.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 183536163
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '240.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1', '12.br1.a1', '12.bs1.a1', '12.bv1.a1', '12.bw1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.k1.a1', '72.a1.a1', '120.bn1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4833, 2907, 4670, 2813, 4220, 6767, 4633, 3069], 'generators': [23, 3669967, 1456, 50803200, 7], 'label': '2880.hl.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536164
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '24.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.e1.a1', '12.f1.a1', '12.bm1.a1', '12.bt1.a1', '12.bx1.a1', '12.by1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '96.f1.a1', '120.bo1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4151, 4425, 4130, 5334, 4048, 6085, 2043, 3899], 'generators': [11, 23, 3669143, 50803200, 7], 'label': '2880.hl.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.b1.a1', '12.b1.a1', '12.e1.a1', '12.f1.a1'], 'normal_contains': ['48.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '2880.hl', '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': '480.1189'}
  • id: 183536165
    {'ambient': '2880.hl', 'aut_centralizer_order': 30, 'aut_label': '24.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '96.a1.a1', 'complements': ['120.dd1.a1', '120.cu1.a1', '120.ch1.a1', '120.cj1.a1', '120.cf1.a1', '120.cs1.a1', '120.cr1.a1', '120.cg1.a1', '120.ct1.a1', '120.cw1.a1', '120.cv1.a1', '120.db1.a1', '120.cy1.a1', '120.cx1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.b1.a1', '12.bn1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '72.bm1.a1', '96.i1.a1', '120.b1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1194, 6712, 712, 6764, 814, 2907, 646, 7078], 'generators': [11, 23, 5, 50803200, 7], 'label': '2880.hl.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.c1.a1', '12.b1.a1'], 'normal_contains': ['48.b1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 183536166
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.e1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '720.a1.a1', 'complements': ['120.cp1.a1', '120.cq1.a1', '120.cz1.a1', '120.db1.a1', '120.da1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1', '12.cb1.a1', '12.ce1.a1'], 'contains': ['48.a1.a1', '48.j1.a1', '48.n1.a1', '72.bn1.a1', '120.bs1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2364, 3745, 3331, 3650, 2630, 5455, 2814, 4529], 'generators': [23, 1456, 3669863, 50803200, 7], 'label': '2880.hl.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.d1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '24.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536167
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '24.f1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': ['120.cu1.a1', '120.dd1.a1', '120.cj1.a1', '120.ch1.a1', '120.cf1.a1', '120.cr1.a1', '120.cs1.a1', '120.cg1.a1', '120.ct1.a1', '120.cv1.a1', '120.cw1.a1', '120.db1.a1', '120.cy1.a1', '120.cx1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.b1.a1', '12.bo1.a1', '12.cd1.a1'], 'contains': ['48.b1.a1', '72.bp1.a1', '96.q1.a1', '120.bx1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1365, 5909, 806, 5817, 716, 3987, 760, 5997], 'generators': [3669138, 11, 23, 50803200, 7], 'label': '2880.hl.24.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': ['8.f1.a1', '12.b1.a1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536168
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '24.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '120.b1.a1', 'complements': ['120.b1.a1', '120.bx1.a1', '120.bu1.a1', '120.bv1.a1', '120.bz1.a1', '120.ca1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.h1.a1', '12.cg1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '72.bs1.a1', '120.cf1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8113, 1038, 8125, 1337, 6192, 8352, 8641, 1632], 'generators': [8025120, 1440, 3669960, 120, 50803200], 'label': '2880.hl.24.g1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.g1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536169
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '48.g1.a1', '48.j1.a1', '48.y1.a1', '48.bc1.a1', '48.bv1.a1', '72.b1.a1', '120.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5569, -1, 5298, -1, 5617, -1, 8687, -1], 'generators': [127, 3669967, 1447, 50803200, 7], 'label': '2880.hl.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.h1.a1', 'projective_image': '2880.hl', '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': '120.36'}
  • id: 183536170
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 3, 'centralizer': '960.a1.a1', 'complements': ['720.bc1.a1', '720.q1.a1', '720.bi1.a1', '720.s1.a1', '720.bn1.a1', '720.bj1.a1', '720.bf1.a1', '720.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.f1.a1', '12.bv1.a1', '16.i1.a1', '20.h1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6371, 2797, 6426, 2825, 5486, 6598, 2122, 3402], 'generators': [11, 23, 3669967, 1456, 8025137, 50803200, 7], 'label': '2880.hl.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '960.11361'}
  • id: 183536171
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.m1.a1', '12.bp1.a1'], 'contains': ['48.f1.a1', '48.h1.a1', '48.l1.a1', '48.x1.a1', '48.bq1.a1', '72.c1.a1', '120.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3992, -1, 3899, -1, 3885, -1, 5417, -1], 'generators': [1456, 5, 120, 50803200, 16], 'label': '2880.hl.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '2880.hl', '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': '48.35'}
  • id: 183536172
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.f1.a1', '48.k1.a1', '48.n1.a1', '48.y1.a1', '48.bw1.a1', '72.d1.a1', '120.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4660, -1, 4482, -1, 4002, -1, 4366, -1], 'generators': [127, 1447, 3669976, 50803200, 7], 'label': '2880.hl.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.j1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536173
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.n1.a1', '12.bq1.a1'], 'contains': ['48.f1.a1', '48.m1.a1', '48.o1.a1', '48.z1.a1', '48.bx1.a1', '72.e1.a1', '120.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3591, -1, 3594, -1, 3720, -1, 5571, -1], 'generators': [1456, 3669965, 120, 50803200, 16], 'label': '2880.hl.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536174
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '144.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.n1.a1', '12.bp1.a1'], 'contains': ['48.f1.a1', '48.p1.a1', '48.q1.a1', '72.f1.a1', '120.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1774, -1, 1436, -1, 1866, -1, 4014, -1], 'generators': [1456, 9, 120, 50803200, 16], 'label': '2880.hl.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.l1.a1', 'projective_image': '2880.hl', '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': '48.35'}
  • id: 183536175
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.m1.a1', '12.bq1.a1'], 'contains': ['48.f1.a1', '48.r1.a1', '48.s1.a1', '72.g1.a1', '120.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2114, -1, 2018, -1, 2095, -1, 3533, -1], 'generators': [1456, 3669969, 120, 50803200, 16], 'label': '2880.hl.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.m1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536176
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1', '12.s1.a1', '12.br1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.m1.a1', '48.ba1.a1', '48.bs1.a1', '72.h1.a1', '120.i1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5206, -1, 5156, -1, 4778, -1, 8558, -1], 'generators': [3669960, 1456, 5, 50803200, 16], 'label': '2880.hl.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.n1.a1', 'projective_image': '2880.hl', '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': '80.50'}
  • id: 183536209
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.t1.a1', '12.cb1.a1'], 'contains': ['48.n1.a1', '48.o1.a1', '48.p1.a1', '72.bk1.a1', '120.bl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2169, -1, 3216, -1, 2140, -1, 4124, -1], 'generators': [1456, 9, 3669863, 50803200, 16], 'label': '2880.hl.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536177
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.o1.a1', '12.t1.a1', '12.u1.a1', '12.v1.a1', '12.w1.a1', '12.x1.a1'], 'contains': ['48.g1.a1', '48.i1.a1', '48.n1.a1', '48.bc1.a1', '48.bw1.a1', '72.i1.a1', '120.j1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6360, -1, 6441, -1, 4835, -1, 6671, -1], 'generators': [136, 3669967, 1447, 50803200, 7], 'label': '2880.hl.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.o1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536178
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.t1.a1', '12.y1.a1', '12.z1.a1', '12.ba1.a1', '12.bb1.a1', '12.bs1.a1'], 'contains': ['48.g1.a1', '48.l1.a1', '48.o1.a1', '48.bd1.a1', '48.ca1.a1', '72.j1.a1', '120.k1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4577, -1, 4727, -1, 4418, -1, 8501, -1], 'generators': [23, 3669960, 122, 1463, 50803200], 'label': '2880.hl.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536179
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.h1.a1', '12.p1.a1', '12.u1.a1', '12.y1.a1', '12.bc1.a1', '12.bd1.a1'], 'contains': ['48.d1.a1', '48.g1.a1', '48.bg1.a1', '72.k1.a1', '120.l1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8002, -1, 7994, -1, 6636, -1, 8821, -1], 'generators': [8025127, 3669967, 1447, 50803200, 7], 'label': '2880.hl.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536180
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.t1.a1', '12.bc1.a1', '12.be1.a1', '12.bf1.a1', '12.bg1.a1', '12.br1.a1'], 'contains': ['48.g1.a1', '48.p1.a1', '48.r1.a1', '72.l1.a1', '120.m1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1852, -1, 1607, -1, 3463, -1, 5679, -1], 'generators': [3669960, 1456, 9, 50803200, 16], 'label': '2880.hl.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536181
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['720.bc1.a1', '720.q1.a1', '720.bd1.a1', '720.bf1.a1', '720.bj1.a1', '720.bn1.a1', '720.bi1.a1', '720.s1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '12.bw1.a1', '12.by1.a1', '12.ca1.a1', '16.j1.a1', '20.i1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6125, 3697, 6217, 4789, 5769, 4782, 2415, 5218], 'generators': [11, 23, 3669967, 1456, 8025253, 50803200, 7], 'label': '2880.hl.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536182
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.j1.a1', '12.q1.a1', '12.v1.a1', '12.z1.a1', '12.be1.a1', '12.bh1.a1'], 'contains': ['48.g1.a1', '48.bg1.a1', '72.m1.a1', '120.n1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9875, -1, 9142, -1, 7684, -1, 8321, -1], 'generators': [3669967, 8025136, 1447, 50803200, 7], 'label': '2880.hl.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536183
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.h1.a1', '12.r1.a1', '12.v1.a1', '12.ba1.a1', '12.bf1.a1', '12.bi1.a1'], 'contains': ['48.e1.a1', '48.g1.a1', '48.bi1.a1', '72.n1.a1', '120.o1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9077, -1, 8936, -1, 7314, -1, 8780, -1], 'generators': [3669967, 1447, 8025247, 50803200, 7], 'label': '2880.hl.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536184
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.o1.a1', '12.bd1.a1', '12.bh1.a1', '12.bi1.a1', '12.bj1.a1', '12.bs1.a1'], 'contains': ['48.g1.a1', '48.q1.a1', '48.s1.a1', '72.o1.a1', '120.p1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1997, -1, 1965, -1, 3350, -1, 5521, -1], 'generators': [23, 3669960, 130, 1463, 50803200], 'label': '2880.hl.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536185
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.q1.a1', '12.w1.a1', '12.bb1.a1', '12.bc1.a1', '12.bi1.a1', '12.bv1.a1'], 'contains': ['48.g1.a1', '48.cb1.a1', '72.p1.a1', '120.q1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6810, -1, 6821, -1, 6345, -1, 8605, -1], 'generators': [3669967, 1447, 8025137, 50803200, 7], 'label': '2880.hl.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536186
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.p1.a1', '12.x1.a1', '12.ba1.a1', '12.be1.a1', '12.bj1.a1', '12.bv1.a1'], 'contains': ['48.g1.a1', '48.bh1.a1', '72.q1.a1', '120.r1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9117, -1, 8865, -1, 6822, -1, 8285, -1], 'generators': [3669967, 1447, 8025126, 50803200, 7], 'label': '2880.hl.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536187
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.j1.a1', '12.s1.a1', '12.u1.a1', '12.bb1.a1', '12.bg1.a1', '12.bj1.a1'], 'contains': ['48.g1.a1', '48.bi1.a1', '72.r1.a1', '120.s1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9266, -1, 9440, -1, 7989, -1, 8361, -1], 'generators': [8025256, 3669967, 1447, 50803200, 7], 'label': '2880.hl.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536188
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.r1.a1', '12.w1.a1', '12.y1.a1', '12.bg1.a1', '12.bh1.a1', '12.bw1.a1'], 'contains': ['48.g1.a1', '48.bj1.a1', '72.s1.a1', '120.t1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8648, -1, 8523, -1, 6415, -1, 8406, -1], 'generators': [23, 3669960, 1463, 8025261, 50803200], 'label': '2880.hl.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536189
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.s1.a1', '12.x1.a1', '12.z1.a1', '12.bd1.a1', '12.bf1.a1', '12.bw1.a1'], 'contains': ['48.g1.a1', '48.cc1.a1', '72.t1.a1', '120.u1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6935, -1, 6631, -1, 6069, -1, 8450, -1], 'generators': [23, 3669960, 1463, 8025253, 50803200], 'label': '2880.hl.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536190
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.206', 'aut_weyl_index': 30, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.bk1.a1', '12.bp1.a1'], 'contains': ['48.h1.a1', '48.i1.a1', '48.q1.a1', '72.u1.a1', '120.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3666, -1, 3729, -1, 3305, -1, 3832, -1], 'generators': [127, 1456, 5, 50803200, 16], 'label': '2880.hl.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 183536191
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.bk1.a1', '12.cb1.a1'], 'contains': ['48.h1.a1', '48.j1.a1', '48.o1.a1', '48.br1.a1', '48.bt1.a1', '72.v1.a1', '120.w1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3822, -1, 4038, -1, 3829, -1, 5474, -1], 'generators': [1456, 5, 3669856, 50803200, 16], 'label': '2880.hl.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536208
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.o1.a1', '12.ce1.a1'], 'contains': ['48.m1.a1', '48.n1.a1', '48.q1.a1', '72.bj1.a1', '120.bk1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3083, -1, 2460, -1, 3162, -1, 4052, -1], 'generators': [1456, 3669863, 3669965, 50803200, 16], 'label': '2880.hl.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536192
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.j1.a1', '4.k1.a1', '6.k1.a1', '6.n1.a1', '8.h1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2155, 6877, 1653, 6971, 1235, 2738, 1106, 7258], 'generators': [11, 124, 23, 3669967, 1456, 5, 50803200, 7], 'label': '2880.hl.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.a1', '4.d1.a1', '4.e1.a1', '4.j1.a1', '4.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '2880.hl', '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': '2880.hl'}
  • id: 183536193
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.j1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['720.bl1.a1', '720.z1.a1', '720.bm1.a1', '720.bb1.a1', '720.w1.a1', '720.x1.a1', '720.y1.a1', '720.ba1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.g1.a1', '12.cb1.a1', '12.cc1.a1', '16.k1.a1', '20.j1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1421, 8708, 1251, 8736, 1152, 1129, 512, 8871], 'generators': [11, 23, 1456, 5, 3669848, 50803200, 7], 'label': '2880.hl.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536194
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.bk1.a1', '12.br1.a1'], 'contains': ['48.h1.a1', '48.k1.a1', '48.r1.a1', '72.w1.a1', '120.x1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3862, -1, 3959, -1, 3588, -1, 3642, -1], 'generators': [3669967, 1456, 5, 50803200, 16], 'label': '2880.hl.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}
  • id: 183536195
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.o1.a1', '12.cb1.a1'], 'contains': ['48.h1.a1', '48.n1.a1', '48.s1.a1', '72.x1.a1', '120.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3894, -1, 3832, -1, 3425, -1, 3572, -1], 'generators': [1456, 5, 3669863, 50803200, 16], 'label': '2880.hl.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536196
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.bk1.a1', '12.bl1.a1'], 'contains': ['48.i1.a1', '48.j1.a1', '48.k1.a1', '48.bv1.a1', '48.bw1.a1', '72.y1.a1', '120.z1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4474, -1, 4344, -1, 3945, -1, 4878, -1], 'generators': [136, 1447, 3669976, 50803200, 7], 'label': '2880.hl.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536197
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.206', 'aut_weyl_index': 30, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.bl1.a1', '12.bp1.a1'], 'contains': ['48.i1.a1', '48.l1.a1', '48.p1.a1', '72.z1.a1', '120.ba1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2402, -1, 2429, -1, 2777, -1, 4315, -1], 'generators': [127, 1456, 9, 50803200, 16], 'label': '2880.hl.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 183536198
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.bl1.a1', '12.bq1.a1'], 'contains': ['48.i1.a1', '48.m1.a1', '48.s1.a1', '72.ba1.a1', '120.bb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3340, -1, 3057, -1, 3193, -1, 4240, -1], 'generators': [127, 1456, 3669965, 50803200, 16], 'label': '2880.hl.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536199
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.bk1.a1', '12.bq1.a1'], 'contains': ['48.i1.a1', '48.o1.a1', '48.r1.a1', '72.bb1.a1', '120.bc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2572, -1, 3377, -1, 2904, -1, 3757, -1], 'generators': [127, 1456, 3669969, 50803200, 16], 'label': '2880.hl.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536200
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.bl1.a1', '12.ce1.a1'], 'contains': ['48.j1.a1', '48.l1.a1', '48.m1.a1', '48.bz1.a1', '48.cd1.a1', '72.bc1.a1', '120.bd1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3737, -1, 3797, -1, 3776, -1, 5628, -1], 'generators': [1456, 3669856, 3669965, 50803200, 16], 'label': '2880.hl.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536201
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.bl1.a1', '12.cb1.a1'], 'contains': ['48.j1.a1', '48.p1.a1', '48.s1.a1', '72.bd1.a1', '120.be1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1896, -1, 1759, -1, 1982, -1, 4202, -1], 'generators': [1456, 9, 3669856, 50803200, 16], 'label': '2880.hl.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536202
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.bk1.a1', '12.ce1.a1'], 'contains': ['48.j1.a1', '48.q1.a1', '48.r1.a1', '72.be1.a1', '120.bf1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1950, -1, 1695, -1, 2020, -1, 3725, -1], 'generators': [1456, 3669856, 3669969, 50803200, 16], 'label': '2880.hl.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536203
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.bl1.a1', '12.bs1.a1'], 'contains': ['48.k1.a1', '48.l1.a1', '48.s1.a1', '72.bf1.a1', '120.bg1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2511, -1, 3118, -1, 2936, -1, 3908, -1], 'generators': [23, 3669967, 122, 1463, 50803200], 'label': '2880.hl.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536204
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.k1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['720.z1.a1', '720.bl1.a1', '720.bb1.a1', '720.bm1.a1', '720.y1.a1', '720.ba1.a1', '720.w1.a1', '720.x1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.f1.a1', '12.cd1.a1', '12.ce1.a1', '16.l1.a1', '20.k1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1981, 7220, 1549, 7246, 998, 2507, 580, 7493], 'generators': [11, 23, 1456, 3669969, 3669848, 50803200, 7], 'label': '2880.hl.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.a1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536205
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bl1.a1', '12.br1.a1'], 'contains': ['48.k1.a1', '48.m1.a1', '48.p1.a1', '72.bg1.a1', '120.bh1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3252, -1, 1571, -1, 3087, -1, 4158, -1], 'generators': [3669967, 1456, 9, 50803200, 16], 'label': '2880.hl.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}
  • id: 183536206
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bk1.a1', '12.bs1.a1'], 'contains': ['48.k1.a1', '48.o1.a1', '48.q1.a1', '72.bh1.a1', '120.bi1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2230, -1, 3265, -1, 2214, -1, 3940, -1], 'generators': [23, 3669967, 130, 1463, 50803200], 'label': '2880.hl.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536207
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.t1.a1', '12.ce1.a1'], 'contains': ['48.l1.a1', '48.n1.a1', '48.r1.a1', '72.bi1.a1', '120.bj1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3117, -1, 2066, -1, 3049, -1, 3604, -1], 'generators': [1456, 3669863, 3669969, 50803200, 16], 'label': '2880.hl.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536210
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1'], 'contains': ['48.b1.a1', '72.bl1.a1', '96.e1.a1', '120.bm1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1535, -1, 863, -1, 487, -1, 876, -1], 'generators': [11, 124, 23, 50803200, 7], 'label': '2880.hl.24.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 183536211
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.bu1.a1', '12.bz1.a1', '12.ca1.a1'], 'contains': ['48.t1.a1', '72.a1.a1', '96.g1.a1', '120.bp1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4212, -1, 4193, -1, 4131, -1, 1972, -1], 'generators': [23, 1460, 3669964, 50803200, 7], 'label': '2880.hl.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '24.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536212
    {'ambient': '2880.hl', 'aut_centralizer_order': 30, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.45', 'aut_weyl_index': 90, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.bp1.a1', '12.br1.a1', '12.cb1.a1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.p1.a1', '72.bm1.a1', '120.bq1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1425, -1, 1154, -1, 1653, -1, 2861, -1], 'generators': [23, 1456, 5, 50803200, 7], 'label': '2880.hl.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '32.45'}
  • id: 183536213
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.bm1.a1', '12.cc1.a1', '12.cd1.a1'], 'contains': ['48.b1.a1', '72.bn1.a1', '96.k1.a1', '120.br1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1591, -1, 1335, -1, 676, -1, 585, -1], 'generators': [11, 23, 3669848, 50803200, 7], 'label': '2880.hl.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536214
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.206', 'aut_weyl_index': 30, 'centralizer': '288.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bp1.a1', '12.bs1.a1', '12.ce1.a1'], 'contains': ['48.a1.a1', '48.l1.a1', '48.q1.a1', '72.bo1.a1', '120.bt1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1696, -1, 1293, -1, 1609, -1, 2950, -1], 'generators': [23, 122, 1456, 50803200, 7], 'label': '2880.hl.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 183536215
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '12.cf1.a1', '12.cg1.a1', '20.l1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5816, -1, 5744, -1, 5421, -1, 2359, -1], 'generators': [8025121, 124, 3, 5, 1440, 3669960, 50803200], 'label': '2880.hl.4.l1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '4.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536216
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bn1.a1', '12.bt1.a1', '12.cd1.a1'], 'contains': ['48.b1.a1', '72.bo1.a1', '96.n1.a1', '120.bu1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1232, -1, 830, -1, 639, -1, 826, -1], 'generators': [11, 23, 122, 50803200, 7], 'label': '2880.hl.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 183536217
    {'ambient': '2880.hl', 'aut_centralizer_order': 5, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bu1.a1'], 'contains': ['48.t1.a1', '72.bo1.a1', '96.o1.a1', '120.bv1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1321, -1, 1060, -1, 932, -1, 951, -1], 'generators': [23, 122, 1460, 50803200, 7], 'label': '2880.hl.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '24.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 183536218
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bq1.a1', '12.br1.a1', '12.ce1.a1'], 'contains': ['48.a1.a1', '48.m1.a1', '48.r1.a1', '72.bp1.a1', '120.bw1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1816, -1, 1392, -1, 1765, -1, 2906, -1], 'generators': [23, 1456, 3669969, 50803200, 7], 'label': '2880.hl.24.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}
  • id: 183536219
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.bq1.a1', '12.bs1.a1', '12.cb1.a1'], 'contains': ['48.a1.a1', '48.o1.a1', '48.s1.a1', '72.bq1.a1', '120.by1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1735, -1, 1533, -1, 1727, -1, 2773, -1], 'generators': [23, 1456, 3669850, 50803200, 7], 'label': '2880.hl.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536220
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.bo1.a1', '12.bt1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '72.bq1.a1', '96.t1.a1', '120.bz1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1256, -1, 769, -1, 784, -1, 616, -1], 'generators': [11, 23, 3669850, 50803200, 7], 'label': '2880.hl.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536221
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.bu1.a1'], 'contains': ['48.t1.a1', '72.bq1.a1', '96.u1.a1', '120.ca1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1345, -1, 1086, -1, 845, -1, 921, -1], 'generators': [23, 1460, 3669850, 50803200, 7], 'label': '2880.hl.24.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '24.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536222
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '8.h1.a1', '12.cf1.a1'], 'contains': ['48.u1.a1', '48.v1.a1', '48.w1.a1', '48.bb1.a1', '48.be1.a1', '48.bu1.a1', '48.by1.a1', '72.br1.a1', '120.cb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2974, -1, 2867, -1, 1417, -1, 1183, -1], 'generators': [124, 5, 3669120, 3, 50803200], 'label': '2880.hl.24.cc1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536223
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '8.i1.a1', '12.cf1.a1'], 'contains': ['48.u1.a1', '48.bk1.a1', '48.bl1.a1', '72.bs1.a1', '120.cc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5343, -1, 5452, -1, 4901, -1, 2573, -1], 'generators': [3669120, 128, 8023692, 12, 50803200], 'label': '2880.hl.24.cd1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536224
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '8.j1.a1', '12.cf1.a1'], 'contains': ['48.u1.a1', '48.bm1.a1', '48.bn1.a1', '72.bu1.a1', '120.cd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6274, -1, 6366, -1, 5313, -1, 2532, -1], 'generators': [8023681, 124, 3669120, 3, 50803200], 'label': '2880.hl.24.ce1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.ce1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536225
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.g1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.x1.a1', '48.z1.a1', '48.ba1.a1', '48.bd1.a1', '48.br1.a1', '48.bz1.a1', '72.br1.a1', '120.ce1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4376, -1, 4436, -1, 4319, -1, 9586, -1], 'generators': [1440, 3669960, 5, 120, 50803200], 'label': '2880.hl.24.cf1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536226
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '10.d1.a1', '10.e1.a1', '10.f1.a1', '10.g1.a1', '15.a1.a1', '15.b1.a1', '20.l1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5912, -1, 5878, -1, 5423, -1, 1671, -1], 'generators': [11, 124, 23, 3669967, 1456, 5, 8025137, 7], 'label': '2880.hl.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536227
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.j1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.bg1.a1', '48.bi1.a1', '72.bt1.a1', '120.cg1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9837, -1, 9391, -1, 7871, -1, 9351, -1], 'generators': [1440, 8025127, 3669960, 120, 50803200], 'label': '2880.hl.24.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.cg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536228
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.l1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.c1.a1', '48.bh1.a1', '48.bj1.a1', '72.bu1.a1', '120.ch1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8882, -1, 8811, -1, 6309, -1, 8982, -1], 'generators': [1440, 3669960, 120, 8025126, 50803200], 'label': '2880.hl.24.ch1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.ch1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536229
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1'], 'contains': ['48.x1.a1', '48.y1.a1', '48.z1.a1', '48.bs1.a1', '48.bt1.a1', '48.ca1.a1', '48.cd1.a1', '72.bv1.a1', '120.ci1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4911, -1, 4790, -1, 4572, -1, 9776, -1], 'generators': [1440, 5, 3669976, 120, 50803200], 'label': '2880.hl.24.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.ci1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536230
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1'], 'contains': ['48.y1.a1', '48.cb1.a1', '48.cc1.a1', '72.bw1.a1', '120.cj1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6507, -1, 6513, -1, 5963, -1, 9540, -1], 'generators': [1440, 3669967, 8025137, 120, 50803200], 'label': '2880.hl.24.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.cj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536231
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.ba1.a1', '48.bc1.a1', '48.bd1.a1', '48.bq1.a1', '48.bt1.a1', '48.bx1.a1', '48.cd1.a1', '72.bx1.a1', '120.ck1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5082, -1, 5068, -1, 4665, -1, 9643, -1], 'generators': [136, 1440, 3669960, 5, 50803200], 'label': '2880.hl.24.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.ck1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536232
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.p1.a1', '12.cg1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.ba1.a1', '48.bh1.a1', '72.by1.a1', '120.cl1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8044, -1, 8269, -1, 6229, -1, 9055, -1], 'generators': [1440, 3669960, 5, 8025125, 50803200], 'label': '2880.hl.24.cl1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536233
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.ch1.a1', '12.cj1.a1'], 'contains': ['48.ba1.a1', '48.bg1.a1', '48.bh1.a1', '72.bz1.a1', '120.cm1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9418, -1, 9113, -1, 7468, -1, 9468, -1], 'generators': [1440, 3669960, 5, 8025134, 50803200], 'label': '2880.hl.24.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536234
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.r1.a1', '12.cg1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.ba1.a1', '48.bj1.a1', '72.ca1.a1', '120.cn1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8463, -1, 8327, -1, 6269, -1, 9131, -1], 'generators': [1440, 3669960, 5, 8025245, 50803200], 'label': '2880.hl.24.cn1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536235
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.ch1.a1', '12.ci1.a1'], 'contains': ['48.ba1.a1', '48.bi1.a1', '48.bj1.a1', '72.cb1.a1', '120.co1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9190, -1, 9175, -1, 6946, -1, 9391, -1], 'generators': [1440, 3669960, 5, 8025254, 50803200], 'label': '2880.hl.24.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.co1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536236
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.k1.a1', '12.cf1.a1'], 'contains': ['48.bb1.a1', '48.bk1.a1', '48.bm1.a1', '72.by1.a1', '120.cp1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5650, -1, 5802, -1, 4972, -1, 2146, -1], 'generators': [11, 5, 3669120, 8023686, 50803200], 'label': '2880.hl.24.cp1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '24.cp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536237
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '720.a1.a1', 'complements': ['480.h1.a1', '480.q1.a1', '480.n1.a1', '480.o1.a1', '480.t1.a1', '480.u1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.h1.a1', '12.j1.a1', '12.u1.a1', '12.v1.a1', '18.j1.a1', '30.m1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8172, 476, 8374, 449, 7657, 9585, 6417, 415], 'generators': [127, 23, 3669967, 8025136, 1456, 50803200, 7], 'label': '2880.hl.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536238
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1.a1', '8.l1.a1', '12.cf1.a1'], 'contains': ['48.bb1.a1', '48.bl1.a1', '48.bn1.a1', '72.ca1.a1', '120.cq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5752, -1, 6051, -1, 5008, -1, 2447, -1], 'generators': [11, 5, 3669120, 8025261, 50803200], 'label': '2880.hl.24.cq1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536239
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.u1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bc1.a1', '48.bi1.a1', '72.cc1.a1', '120.cr1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8400, -1, 8425, -1, 7274, -1, 9171, -1], 'generators': [127, 8025120, 1440, 3669960, 50803200], 'label': '2880.hl.24.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.cr1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536240
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.v1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bc1.a1', '48.bg1.a1', '72.cd1.a1', '120.cs1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9360, -1, 8903, -1, 7540, -1, 9279, -1], 'generators': [127, 1440, 8025127, 3669960, 50803200], 'label': '2880.hl.24.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.cs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536241
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.u1.a1', '12.v1.a1'], 'contains': ['48.bc1.a1', '48.bg1.a1', '48.bi1.a1', '72.ce1.a1', '120.ct1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9689, -1, 9363, -1, 7948, -1, 9243, -1], 'generators': [127, 1440, 3669960, 8025136, 50803200], 'label': '2880.hl.24.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.ct1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536242
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.bc1.a1', '48.bh1.a1', '48.bj1.a1', '72.cf1.a1', '120.cu1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8844, -1, 8626, -1, 6744, -1, 9207, -1], 'generators': [127, 1440, 3669960, 8025126, 50803200], 'label': '2880.hl.24.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536243
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.y1.a1', '12.cg1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bd1.a1', '48.bj1.a1', '72.cg1.a1', '120.cv1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8270, -1, 8096, -1, 5999, -1, 9091, -1], 'generators': [8025120, 1440, 3669960, 8025261, 50803200], 'label': '2880.hl.24.cv1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536244
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '12.ch1.a1', '12.cj1.a1'], 'contains': ['48.bd1.a1', '48.bg1.a1', '48.bj1.a1', '72.ch1.a1', '120.cw1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9389, -1, 9067, -1, 7172, -1, 9432, -1], 'generators': [1440, 3669960, 8025143, 8025261, 50803200], 'label': '2880.hl.24.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536245
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.ba1.a1', '12.cg1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bd1.a1', '48.bh1.a1', '72.ci1.a1', '120.cx1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8816, -1, 8556, -1, 6522, -1, 9018, -1], 'generators': [1440, 3669960, 122, 8025122, 50803200], 'label': '2880.hl.24.cx1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536246
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '12.ch1.a1', '12.ci1.a1'], 'contains': ['48.bd1.a1', '48.bh1.a1', '48.bi1.a1', '72.cj1.a1', '120.cy1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9315, -1, 9289, -1, 7504, -1, 9315, -1], 'generators': [1440, 3669960, 122, 8025141, 50803200], 'label': '2880.hl.24.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cy1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536247
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '8.m1.a1', '12.cf1.a1'], 'contains': ['48.be1.a1', '48.bk1.a1', '48.bn1.a1', '72.cg1.a1', '120.cz1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5617, -1, 5608, -1, 4732, -1, 2381, -1], 'generators': [8025242, 3669120, 8023692, 12, 50803200], 'label': '2880.hl.24.cz1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536248
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': ['480.a1.a1', '480.i1.a1', '480.k1.a1', '480.r1.a1', '480.m1.a1', '480.s1.a1', '480.o1.a1', '480.u1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.f1.a1', '18.l1.a1', '24.cp1.a1', '30.q1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5516, 2564, 5720, 3029, 4927, 7268, 2076, 2732], 'generators': [11, 23, 8023697, 5, 3669143, 50803200, 7], 'label': '2880.hl.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.b1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536249
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '8.n1.a1', '12.cf1.a1'], 'contains': ['48.be1.a1', '48.bl1.a1', '48.bm1.a1', '72.ci1.a1', '120.da1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6020, -1, 6131, -1, 5354, -1, 2237, -1], 'generators': [122, 3669120, 8023686, 12, 50803200], 'label': '2880.hl.24.da1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.da1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536250
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '8.m1.a1'], 'contains': ['48.bf1.a1', '48.bo1.a1', '48.bp1.a1', '72.cg1.a1', '120.db1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5937, -1, 5973, -1, 5856, -1, 2283, -1], 'generators': [8025132, 1452, 8025242, 3669968, 50803200], 'label': '2880.hl.24.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.db1.a1', 'old_label': '24.db1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536251
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1'], 'contains': ['48.bq1.a1', '48.br1.a1', '48.bs1.a1', '48.bv1.a1', '48.bx1.a1', '48.bz1.a1', '48.ca1.a1', '72.ck1.a1', '120.dc1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4980, -1, 4963, -1, 4516, -1, 9700, -1], 'generators': [136, 1440, 5, 3669976, 50803200], 'label': '2880.hl.24.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.dc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536252
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1'], 'contains': ['48.bv1.a1', '48.cb1.a1', '48.cc1.a1', '72.cl1.a1', '120.dd1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6452, -1, 6479, -1, 5927, -1, 9504, -1], 'generators': [127, 1440, 3669967, 8025137, 50803200], 'label': '2880.hl.24.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.dd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536253
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '15.b1.a1'], 'contains': ['60.a1.a1', '60.b1.a1', '60.f1.a1', '60.j1.a1', '60.l1.a1', '60.s1.a1', '60.u1.a1', '60.cg1.a1', '60.ch1.a1', '60.ci1.a1', '60.cj1.a1', '90.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8623, -1, 9658, -1, 9343, -1, 6675, -1], 'generators': [3669960, 1456, 5, 8025134, 120, 16], 'label': '2880.hl.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536254
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '15.b1.a1'], 'contains': ['60.a1.a1', '60.d1.a1', '60.e1.a1', '60.k1.a1', '60.m1.a1', '60.t1.a1', '60.v1.a1', '90.b1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6822, -1, 7024, -1, 8380, -1, 6901, -1], 'generators': [3669960, 1456, 5, 8025138, 120, 16], 'label': '2880.hl.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536255
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.b1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.e1.a1', '60.w1.a1', '60.x1.a1', '60.z1.a1', '60.bc1.a1', '90.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7351, -1, 7440, -1, 8266, -1, 6130, -1], 'generators': [3669960, 1456, 9, 8025138, 120, 16], 'label': '2880.hl.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536256
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.b1.a1'], 'contains': ['60.c1.a1', '60.d1.a1', '60.f1.a1', '60.y1.a1', '60.ba1.a1', '60.bb1.a1', '60.bd1.a1', '90.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9455, -1, 9808, -1, 9101, -1, 5987, -1], 'generators': [3669960, 1456, 9, 8025134, 120, 16], 'label': '2880.hl.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536257
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '15.b1.a1'], 'contains': ['60.i1.a1', '60.j1.a1', '60.m1.a1', '60.o1.a1', '60.r1.a1', '60.x1.a1', '60.bd1.a1', '90.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7812, -1, 7664, -1, 8591, -1, 6086, -1], 'generators': [127, 3669960, 1456, 5, 8025134, 16], 'label': '2880.hl.30.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536258
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '15.b1.a1'], 'contains': ['60.i1.a1', '60.k1.a1', '60.l1.a1', '60.p1.a1', '60.q1.a1', '60.bb1.a1', '60.bc1.a1', '90.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7173, -1, 8020, -1, 8725, -1, 6177, -1], 'generators': [127, 3669960, 1456, 5, 8025138, 16], 'label': '2880.hl.30.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536259
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.g1.a1', '12.h1.a1', '12.l1.a1', '12.p1.a1', '12.r1.a1', '12.y1.a1', '12.ba1.a1', '12.cg1.a1', '12.ch1.a1', '12.ci1.a1', '12.cj1.a1', '18.a1.a1', '30.a1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8294, -1, 8300, -1, 6856, -1, 8391, -1], 'generators': [3669960, 1456, 5, 8025134, 120, 50803200, 16], 'label': '2880.hl.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.c1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536260
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '15.b1.a1'], 'contains': ['60.n1.a1', '60.o1.a1', '60.q1.a1', '60.s1.a1', '60.v1.a1', '60.w1.a1', '60.ba1.a1', '90.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7525, -1, 7855, -1, 8656, -1, 6310, -1], 'generators': [127, 3669960, 1456, 9, 8025138, 16], 'label': '2880.hl.30.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536261
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '15.b1.a1'], 'contains': ['60.n1.a1', '60.p1.a1', '60.r1.a1', '60.t1.a1', '60.u1.a1', '60.y1.a1', '60.z1.a1', '90.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8036, -1, 7581, -1, 8438, -1, 6037, -1], 'generators': [127, 3669960, 1456, 9, 8025134, 16], 'label': '2880.hl.30.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536262
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.bg1.a1', '60.bh1.a1', '60.bi1.a1', '60.bn1.a1', '60.bp1.a1', '60.cc1.a1', '60.cd1.a1', '90.i1.a1', '120.cb1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [717, -1, 631, -1, 731, -1, 1137, -1], 'generators': [11, 124, 23, 5, 3669143, 7], 'label': '2880.hl.30.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536263
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.bg1.a1', '60.bv1.a1', '60.bw1.a1', '90.j1.a1', '120.cc1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5369, -1, 5444, -1, 4835, -1, 1872, -1], 'generators': [11, 124, 23, 3669143, 8023692, 7], 'label': '2880.hl.30.j1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536264
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.bg1.a1', '60.bx1.a1', '60.by1.a1', '90.k1.a1', '120.cd1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6258, -1, 6297, -1, 5279, -1, 1684, -1], 'generators': [11, 124, 23, 8023697, 3669143, 7], 'label': '2880.hl.30.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536265
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '10.a1.a1', '15.b1.a1'], 'contains': ['60.a1.a1', '60.c1.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1', '60.n1.a1', '60.be1.a1', '60.bf1.a1', '60.bj1.a1', '60.bk1.a1', '60.bl1.a1', '60.bm1.a1', '60.bo1.a1', '60.cb1.a1', '60.ce1.a1', '90.i1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2408, -1, 2711, -1, 3054, -1, 3378, -1], 'generators': [127, 23, 3669967, 1456, 5, 7], 'label': '2880.hl.30.l1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536266
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '30.m1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.b1.a1'], 'contains': ['60.b1.a1', '60.d1.a1', '60.o1.a1', '60.p1.a1', '60.bj1.a1', '60.br1.a1', '60.bs1.a1', '90.j1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8464, -1, 8978, -1, 9643, -1, 5667, -1], 'generators': [127, 23, 3669967, 8025136, 1456, 7], 'label': '2880.hl.30.m1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536267
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1.a1', '10.c1.a1', '15.b1.a1'], 'contains': ['60.e1.a1', '60.f1.a1', '60.q1.a1', '60.r1.a1', '60.bj1.a1', '60.bt1.a1', '60.bu1.a1', '90.k1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6773, -1, 7064, -1, 8117, -1, 5611, -1], 'generators': [127, 23, 3669967, 1456, 8025137, 7], 'label': '2880.hl.30.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536268
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '30.o1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1.a1', '10.d1.a1', '15.b1.a1'], 'contains': ['60.j1.a1', '60.k1.a1', '60.w1.a1', '60.y1.a1', '60.bm1.a1', '60.br1.a1', '60.bt1.a1', '90.l1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7245, -1, 7779, -1, 8547, -1, 5417, -1], 'generators': [23, 3669967, 1456, 5, 8025134, 7], 'label': '2880.hl.30.o1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536269
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.p1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '10.e1.a1', '15.b1.a1'], 'contains': ['60.l1.a1', '60.m1.a1', '60.z1.a1', '60.ba1.a1', '60.bm1.a1', '60.bs1.a1', '60.bu1.a1', '90.m1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7920, -1, 7160, -1, 8330, -1, 5563, -1], 'generators': [23, 3669967, 1456, 5, 8025254, 7], 'label': '2880.hl.30.p1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536270
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.g1.a1', '12.j1.a1', '12.k1.a1', '12.q1.a1', '12.s1.a1', '12.z1.a1', '12.bb1.a1', '18.b1.a1', '30.b1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6991, -1, 6909, -1, 7424, -1, 7813, -1], 'generators': [3669960, 1456, 5, 8025138, 120, 50803200, 16], 'label': '2880.hl.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.d1.a1', 'projective_image': '2880.hl', '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': '480.1197'}
  • id: 183536271
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '30.q1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.d1.a1', '15.a1.a1'], 'contains': ['60.bn1.a1', '60.bv1.a1', '60.bx1.a1', '90.l1.a1', '120.cp1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5698, -1, 5733, -1, 4915, -1, 1490, -1], 'generators': [11, 23, 8023697, 5, 3669143, 7], 'label': '2880.hl.30.q1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536272
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.r1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1.a1', '10.e1.a1', '15.a1.a1'], 'contains': ['60.bn1.a1', '60.bw1.a1', '60.by1.a1', '90.m1.a1', '120.cq1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5898, -1, 6017, -1, 5028, -1, 1623, -1], 'generators': [11, 23, 5, 8025253, 3669143, 7], 'label': '2880.hl.30.r1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536273
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.s1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1', '10.f1.a1', '15.b1.a1'], 'contains': ['60.s1.a1', '60.t1.a1', '60.x1.a1', '60.bb1.a1', '60.bo1.a1', '60.br1.a1', '60.bu1.a1', '90.n1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7658, -1, 7532, -1, 8201, -1, 5518, -1], 'generators': [23, 3669967, 8025136, 1456, 8025253, 7], 'label': '2880.hl.30.s1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.s1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536274
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.t1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '10.g1.a1', '15.b1.a1'], 'contains': ['60.u1.a1', '60.v1.a1', '60.bc1.a1', '60.bd1.a1', '60.bo1.a1', '60.bs1.a1', '60.bt1.a1', '90.o1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7025, -1, 7968, -1, 8778, -1, 5369, -1], 'generators': [23, 3669967, 122, 1456, 8025133, 7], 'label': '2880.hl.30.t1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536275
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.u1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '10.f1.a1', '15.a1.a1'], 'contains': ['60.bp1.a1', '60.bv1.a1', '60.by1.a1', '90.n1.a1', '120.cz1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5653, -1, 5654, -1, 4778, -1, 1735, -1], 'generators': [11, 23, 8025253, 3669143, 8023692, 7], 'label': '2880.hl.30.u1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.u1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536276
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '30.v1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '10.g1.a1', '15.a1.a1'], 'contains': ['60.bp1.a1', '60.bw1.a1', '60.bx1.a1', '90.o1.a1', '120.da1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6022, -1, 6121, -1, 5340, -1, 1444, -1], 'generators': [11, 23, 8023697, 122, 3669143, 7], 'label': '2880.hl.30.v1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.v1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536277
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '30.w1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '10.f1.a1'], 'contains': ['60.bq1.a1', '60.bz1.a1', '60.ca1.a1', '90.n1.a1', '120.db1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5968, -1, 5852, -1, 5876, -1, 1929, -1], 'generators': [23, 8025132, 1460, 3669964, 8025253, 7], 'label': '2880.hl.30.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.w1.a1', 'old_label': '30.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.w1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536278
    {'ambient': '2880.hl', 'aut_centralizer_order': 15, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.e1.a1', '160.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2774, -1, 1963, -1, 387, -1, 599, -1], 'generators': [124, 1440, 3, 50803200], 'label': '2880.hl.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 183536279
    {'ambient': '2880.hl', 'aut_centralizer_order': 9, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '16.b1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '96.b1.a1', '96.f1.a1', '96.g1.a1', '160.b1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4178, -1, 4204, -1, 4533, -1, 2008, -1], 'generators': [11, 1440, 3669960, 50803200], 'label': '2880.hl.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536280
    {'ambient': '2880.hl', 'aut_centralizer_order': 15, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '16.c1.a1', '16.e1.a1', '16.k1.a1'], 'contains': ['64.a1.a1', '96.h1.a1', '96.i1.a1', '160.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3122, -1, 3221, -1, 1338, -1, 378, -1], 'generators': [11, 1440, 5, 50803200], 'label': '2880.hl.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 183536281
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.h1.a1', '12.i1.a1', '12.k1.a1', '12.bc1.a1', '12.bd1.a1', '12.bf1.a1', '12.bi1.a1', '18.c1.a1', '30.c1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7394, -1, 7437, -1, 6538, -1, 7370, -1], 'generators': [3669960, 1456, 9, 8025138, 120, 50803200, 16], 'label': '2880.hl.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536282
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '16.b1.a1', '16.k1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '96.k1.a1', '160.d1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2739, -1, 2050, -1, 441, -1, 223, -1], 'generators': [1440, 12, 3669848, 50803200], 'label': '2880.hl.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536283
    {'ambient': '2880.hl', 'aut_centralizer_order': 5, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.143', 'aut_weyl_index': 20, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '16.c1.a1', '16.f1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.m1.a1', '96.n1.a1', '96.o1.a1', '160.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2809, -1, 2343, -1, 1177, -1, 498, -1], 'generators': [1440, 122, 12, 50803200], 'label': '2880.hl.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 183536284
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '16.d1.a1', '16.e1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.p1.a1', '96.q1.a1', '160.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2695, -1, 1999, -1, 1133, -1, 454, -1], 'generators': [1440, 3669974, 12, 50803200], 'label': '2880.hl.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536285
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '16.d1.a1', '16.f1.a1', '16.k1.a1'], 'contains': ['64.a1.a1', '96.s1.a1', '96.t1.a1', '96.u1.a1', '160.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2840, -1, 2312, -1, 948, -1, 416, -1], 'generators': [1440, 3669842, 12, 50803200], 'label': '2880.hl.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536286
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': ['80.c1.a1', '80.d1.a1', '80.l1.a1', '80.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.e1.a1', '12.bz1.a1', '18.j1.a1', '18.l1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.k1.a1', '72.m1.a1', '180.bl1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8135, 1955, 8126, 2111, 6597, 7636, 5292, 2349], 'generators': [23, 3669143, 8023696, 50803200, 7], 'label': '2880.hl.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.c1.a1', '12.e1.a1'], 'normal_contains': ['72.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536287
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.a1.a1', '18.b1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.e1.a1', '72.h1.a1', '72.j1.a1', '72.v1.a1', '72.bc1.a1', '72.br1.a1', '72.bv1.a1', '72.bx1.a1', '72.ck1.a1', '180.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4642, -1, 4871, -1, 4368, -1, 7827, -1], 'generators': [5, 3669136, 120, 50803200, 16], 'label': '2880.hl.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536288
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.a1.a1', '18.c1.a1', '18.j1.a1'], 'contains': ['72.b1.a1', '72.k1.a1', '72.n1.a1', '72.bs1.a1', '72.bt1.a1', '72.cc1.a1', '72.cd1.a1', '180.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8548, -1, 8607, -1, 7210, -1, 8204, -1], 'generators': [127, 3669120, 8023687, 50803200, 7], 'label': '2880.hl.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '2880.hl', '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': '20.3'}
  • id: 183536289
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.c1.a1', '18.d1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.f1.a1', '72.g1.a1', '72.l1.a1', '72.o1.a1', '72.bd1.a1', '72.be1.a1', '180.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1469, -1, 1412, -1, 1816, -1, 5097, -1], 'generators': [9, 3669136, 120, 50803200, 16], 'label': '2880.hl.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536290
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.b1.a1', '18.d1.a1', '18.j1.a1'], 'contains': ['72.b1.a1', '72.m1.a1', '72.r1.a1', '72.bt1.a1', '72.ce1.a1', '180.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9609, -1, 9482, -1, 7910, -1, 8036, -1], 'generators': [127, 3669120, 8023696, 50803200, 7], 'label': '2880.hl.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536291
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.b1.a1', '18.c1.a1', '18.k1.a1'], 'contains': ['72.b1.a1', '72.p1.a1', '72.t1.a1', '72.bw1.a1', '72.cl1.a1', '180.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6708, -1, 6617, -1, 6112, -1, 8737, -1], 'generators': [127, 8023697, 3669120, 50803200, 7], 'label': '2880.hl.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536292
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.i1.a1', '12.j1.a1', '12.l1.a1', '12.be1.a1', '12.bg1.a1', '12.bh1.a1', '12.bj1.a1', '18.d1.a1', '30.d1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8445, -1, 8538, -1, 7797, -1, 7063, -1], 'generators': [3669960, 1456, 9, 8025134, 120, 50803200, 16], 'label': '2880.hl.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.f1.a1', 'projective_image': '2880.hl', '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': '480.1197'}
  • id: 183536293
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.a1.a1', '18.d1.a1', '18.k1.a1'], 'contains': ['72.b1.a1', '72.q1.a1', '72.s1.a1', '72.bu1.a1', '72.cf1.a1', '180.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9006, -1, 8780, -1, 6783, -1, 7869, -1], 'generators': [127, 3669120, 8023686, 50803200, 7], 'label': '2880.hl.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536294
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.i1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.g1.a1', '72.w1.a1', '72.x1.a1', '72.bf1.a1', '72.bi1.a1', '180.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3312, -1, 3202, -1, 2866, -1, 3687, -1], 'generators': [5, 3669143, 120, 50803200, 16], 'label': '2880.hl.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536295
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '18.i1.a1'], 'contains': ['72.d1.a1', '72.e1.a1', '72.f1.a1', '72.bg1.a1', '72.bh1.a1', '72.bj1.a1', '72.bk1.a1', '180.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2327, -1, 2637, -1, 2318, -1, 4090, -1], 'generators': [9, 3669143, 120, 50803200, 16], 'label': '2880.hl.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536296
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.e1.a1', '18.f1.a1', '18.i1.a1'], 'contains': ['72.h1.a1', '72.i1.a1', '72.o1.a1', '72.u1.a1', '72.x1.a1', '72.ba1.a1', '72.bj1.a1', '180.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3605, -1, 3672, -1, 3629, -1, 5186, -1], 'generators': [127, 5, 3669136, 50803200, 16], 'label': '2880.hl.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536297
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '18.a1.a1', '18.e1.a1', '18.l1.a1'], 'contains': ['72.h1.a1', '72.k1.a1', '72.q1.a1', '72.by1.a1', '72.bz1.a1', '180.j1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8332, -1, 8391, -1, 6861, -1, 8078, -1], 'generators': [8023694, 5, 3669136, 50803200, 16], 'label': '2880.hl.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536298
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.b1.a1', '18.f1.a1', '18.l1.a1'], 'contains': ['72.h1.a1', '72.m1.a1', '72.p1.a1', '180.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6968, -1, 7339, -1, 7025, -1, 7760, -1], 'generators': [5, 8023698, 3669136, 50803200, 16], 'label': '2880.hl.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536299
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '18.a1.a1', '18.f1.a1', '18.m1.a1'], 'contains': ['72.h1.a1', '72.n1.a1', '72.s1.a1', '72.ca1.a1', '72.cb1.a1', '180.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8902, -1, 8650, -1, 6989, -1, 8120, -1], 'generators': [5, 8025254, 3669136, 50803200, 16], 'label': '2880.hl.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536300
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '18.b1.a1', '18.e1.a1', '18.m1.a1'], 'contains': ['72.h1.a1', '72.r1.a1', '72.t1.a1', '180.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7588, -1, 6786, -1, 7717, -1, 7730, -1], 'generators': [5, 8025258, 3669136, 50803200, 16], 'label': '2880.hl.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536301
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1'], 'contains': ['72.i1.a1', '72.j1.a1', '72.l1.a1', '72.z1.a1', '72.bb1.a1', '72.bi1.a1', '72.bk1.a1', '180.n1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2262, -1, 2807, -1, 2567, -1, 5223, -1], 'generators': [127, 9, 3669136, 50803200, 16], 'label': '2880.hl.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536302
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '18.e1.a1', '18.g1.a1', '18.j1.a1'], 'contains': ['72.i1.a1', '72.k1.a1', '72.r1.a1', '72.cc1.a1', '72.ce1.a1', '180.o1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8476, -1, 8737, -1, 7603, -1, 7994, -1], 'generators': [136, 3669120, 8023687, 50803200, 7], 'label': '2880.hl.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536303
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['1440.d1.a1', '1440.i1.a1', '1440.h1.a1', '1440.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.a1.a1', '6.l1.a1', '8.i1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5321, 493, 5277, 647, 5158, 8567, 2521, 1433], 'generators': [8025132, 11, 7, 1456, 23, 124, 3669967, 50803200], 'label': '2880.hl.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.f1.a1', '4.g1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536304
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.o1.a1', '12.p1.a1', '12.s1.a1', '12.u1.a1', '12.x1.a1', '12.bd1.a1', '12.bj1.a1', '18.e1.a1', '30.e1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7891, -1, 7554, -1, 7333, -1, 7293, -1], 'generators': [127, 3669960, 1456, 5, 8025134, 50803200, 16], 'label': '2880.hl.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '2880.hl', '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': '480.1197'}
  • id: 183536305
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '18.f1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.i1.a1', '72.m1.a1', '72.n1.a1', '72.cd1.a1', '72.ce1.a1', '180.p1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9428, -1, 8998, -1, 7645, -1, 7911, -1], 'generators': [136, 3669120, 8023696, 50803200, 7], 'label': '2880.hl.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536306
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '18.f1.a1', '18.g1.a1', '18.k1.a1'], 'contains': ['72.i1.a1', '72.p1.a1', '72.s1.a1', '180.q1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7137, -1, 6949, -1, 6378, -1, 7501, -1], 'generators': [136, 8023697, 3669120, 50803200, 7], 'label': '2880.hl.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536307
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '18.e1.a1', '18.h1.a1', '18.k1.a1'], 'contains': ['72.i1.a1', '72.q1.a1', '72.t1.a1', '180.r1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7751, -1, 6876, -1, 6711, -1, 7398, -1], 'generators': [136, 3669120, 8023686, 50803200, 7], 'label': '2880.hl.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536308
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '18.a1.a1', '18.g1.a1', '18.n1.a1'], 'contains': ['72.j1.a1', '72.k1.a1', '72.s1.a1', '72.cg1.a1', '72.ch1.a1', '180.s1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8366, -1, 8184, -1, 6675, -1, 8162, -1], 'generators': [8023703, 23, 8025261, 3669143, 50803200], 'label': '2880.hl.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536309
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '18.b1.a1', '18.h1.a1', '18.n1.a1'], 'contains': ['72.j1.a1', '72.m1.a1', '72.t1.a1', '180.t1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7629, -1, 6810, -1, 7393, -1, 7700, -1], 'generators': [23, 8025253, 3669143, 8023696, 50803200], 'label': '2880.hl.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536310
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '18.a1.a1', '18.h1.a1', '18.o1.a1'], 'contains': ['72.j1.a1', '72.n1.a1', '72.q1.a1', '72.ci1.a1', '72.cj1.a1', '180.u1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9080, -1, 8916, -1, 7357, -1, 7952, -1], 'generators': [23, 122, 8023701, 3669143, 50803200], 'label': '2880.hl.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536311
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '18.b1.a1', '18.g1.a1', '18.o1.a1'], 'contains': ['72.j1.a1', '72.p1.a1', '72.r1.a1', '180.v1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6996, -1, 7315, -1, 7747, -1, 7790, -1], 'generators': [23, 122, 8023693, 3669143, 50803200], 'label': '2880.hl.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536312
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '18.c1.a1', '18.g1.a1', '18.l1.a1'], 'contains': ['72.k1.a1', '72.l1.a1', '72.p1.a1', '180.w1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7281, -1, 7789, -1, 6558, -1, 7468, -1], 'generators': [8023698, 9, 3669136, 50803200, 16], 'label': '2880.hl.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536313
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '18.c1.a1', '18.e1.a1', '18.n1.a1'], 'contains': ['72.k1.a1', '72.o1.a1', '72.t1.a1', '180.x1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7724, -1, 7279, -1, 6456, -1, 7308, -1], 'generators': [8023703, 23, 8025253, 3669143, 50803200], 'label': '2880.hl.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536314
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '18.d1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.l1.a1', '72.m1.a1', '72.q1.a1', '180.y1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9692, -1, 9029, -1, 7570, -1, 7169, -1], 'generators': [8023694, 9, 3669136, 50803200, 16], 'label': '2880.hl.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536315
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.o1.a1', '12.q1.a1', '12.r1.a1', '12.v1.a1', '12.w1.a1', '12.bh1.a1', '12.bi1.a1', '18.f1.a1', '30.f1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7442, -1, 8040, -1, 7043, -1, 7431, -1], 'generators': [127, 3669960, 1456, 5, 8025138, 50803200, 16], 'label': '2880.hl.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.h1.a1', 'projective_image': '2880.hl', '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': '480.1197'}
  • id: 183536316
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '18.c1.a1', '18.h1.a1', '18.m1.a1'], 'contains': ['72.l1.a1', '72.n1.a1', '72.t1.a1', '180.z1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7946, -1, 7249, -1, 7094, -1, 7272, -1], 'generators': [8025258, 9, 3669136, 50803200, 16], 'label': '2880.hl.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536317
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '18.d1.a1', '18.g1.a1', '18.m1.a1'], 'contains': ['72.l1.a1', '72.r1.a1', '72.s1.a1', '180.ba1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8875, -1, 9411, -1, 7774, -1, 7242, -1], 'generators': [8025254, 9, 3669136, 50803200, 16], 'label': '2880.hl.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536318
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '18.d1.a1', '18.f1.a1', '18.n1.a1'], 'contains': ['72.m1.a1', '72.o1.a1', '72.s1.a1', '180.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8833, -1, 8889, -1, 7244, -1, 7217, -1], 'generators': [23, 8025261, 3669143, 8023696, 50803200], 'label': '2880.hl.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536319
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '18.c1.a1', '18.f1.a1', '18.o1.a1'], 'contains': ['72.n1.a1', '72.o1.a1', '72.p1.a1', '180.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7093, -1, 7718, -1, 7058, -1, 7431, -1], 'generators': [23, 130, 8023693, 3669143, 50803200], 'label': '2880.hl.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536320
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '18.d1.a1', '18.e1.a1', '18.o1.a1'], 'contains': ['72.o1.a1', '72.q1.a1', '72.r1.a1', '180.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9222, -1, 9533, -1, 7841, -1, 7193, -1], 'generators': [23, 130, 8023701, 3669143, 50803200], 'label': '2880.hl.36.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536321
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '18.i1.a1'], 'contains': ['72.u1.a1', '72.v1.a1', '72.w1.a1', '72.y1.a1', '72.bb1.a1', '72.be1.a1', '72.bh1.a1', '180.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3280, -1, 3279, -1, 2737, -1, 3792, -1], 'generators': [127, 5, 3669143, 50803200, 16], 'label': '2880.hl.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536322
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '18.i1.a1'], 'contains': ['72.y1.a1', '72.z1.a1', '72.ba1.a1', '72.bc1.a1', '72.bd1.a1', '72.bf1.a1', '72.bg1.a1', '180.bf1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2557, -1, 1846, -1, 2530, -1, 4275, -1], 'generators': [127, 9, 3669143, 50803200, 16], 'label': '2880.hl.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536323
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.bm1.a1', '18.i1.a1', '18.j1.a1', '18.k1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.d1.a1', '72.i1.a1', '72.y1.a1', '72.bl1.a1', '72.bn1.a1', '180.bg1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4823, -1, 4558, -1, 4171, -1, 4828, -1], 'generators': [127, 23, 3669143, 50803200, 7], 'label': '2880.hl.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536324
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '12.bp1.a1', '18.i1.a1'], 'contains': ['72.c1.a1', '72.f1.a1', '72.u1.a1', '72.z1.a1', '72.bl1.a1', '72.bm1.a1', '72.bo1.a1', '180.bh1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1591, -1, 1157, -1, 1039, -1, 3177, -1], 'generators': [127, 23, 5, 50803200, 7], 'label': '2880.hl.36.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 183536325
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1.a1', '12.bq1.a1', '18.i1.a1'], 'contains': ['72.e1.a1', '72.g1.a1', '72.ba1.a1', '72.bb1.a1', '72.bl1.a1', '72.bp1.a1', '72.bq1.a1', '180.bi1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1917, -1, 1508, -1, 1294, -1, 3132, -1], 'generators': [3669138, 127, 23, 50803200, 7], 'label': '2880.hl.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536326
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.t1.a1', '12.u1.a1', '12.w1.a1', '12.y1.a1', '12.bb1.a1', '12.bc1.a1', '12.bg1.a1', '18.g1.a1', '30.g1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7669, -1, 7995, -1, 7241, -1, 7486, -1], 'generators': [127, 3669960, 1456, 9, 8025138, 50803200, 16], 'label': '2880.hl.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536327
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.br1.a1', '18.i1.a1', '18.l1.a1', '18.m1.a1'], 'contains': ['72.a1.a1', '72.h1.a1', '72.l1.a1', '72.w1.a1', '72.bg1.a1', '72.bm1.a1', '72.bp1.a1', '180.bj1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3168, -1, 1375, -1, 3228, -1, 3974, -1], 'generators': [23, 5, 3669143, 50803200, 7], 'label': '2880.hl.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536328
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '12.bt1.a1', '12.bu1.a1', '18.i1.a1', '18.n1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.j1.a1', '72.o1.a1', '72.bf1.a1', '72.bh1.a1', '72.bo1.a1', '72.bq1.a1', '180.bk1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1746, -1, 2016, -1, 2054, -1, 3873, -1], 'generators': [23, 122, 3669143, 50803200, 7], 'label': '2880.hl.36.bl1.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.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536329
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.bx1.a1', '18.j1.a1', '18.m1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.n1.a1', '72.r1.a1', '180.bm1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9122, -1, 9351, -1, 7807, -1, 5364, -1], 'generators': [8025256, 23, 3669143, 50803200, 7], 'label': '2880.hl.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536330
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bv1.a1', '18.k1.a1', '18.l1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.p1.a1', '72.q1.a1', '180.bn1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6919, -1, 7180, -1, 6489, -1, 5256, -1], 'generators': [23, 8023697, 3669143, 50803200, 7], 'label': '2880.hl.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536331
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '12.by1.a1', '12.ca1.a1', '18.k1.a1', '18.m1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.s1.a1', '72.t1.a1', '180.bo1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7431, -1, 6737, -1, 6032, -1, 5328, -1], 'generators': [23, 8025253, 3669143, 50803200, 7], 'label': '2880.hl.36.bo1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536332
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '12.cc1.a1', '18.i1.a1'], 'contains': ['72.v1.a1', '72.x1.a1', '72.bd1.a1', '72.bk1.a1', '72.bm1.a1', '72.bn1.a1', '72.bq1.a1', '180.bp1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1506, -1, 2378, -1, 1335, -1, 2991, -1], 'generators': [23, 5, 3669863, 50803200, 7], 'label': '2880.hl.36.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536333
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '12.ce1.a1', '18.i1.a1'], 'contains': ['72.bc1.a1', '72.be1.a1', '72.bi1.a1', '72.bj1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '180.bq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1800, -1, 1459, -1, 1568, -1, 3028, -1], 'generators': [3669138, 23, 3669863, 50803200, 7], 'label': '2880.hl.36.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536334
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.a1', '12.cg1.a1', '18.a1.a1'], 'contains': ['72.br1.a1', '72.bs1.a1', '72.bu1.a1', '72.by1.a1', '72.ca1.a1', '72.cg1.a1', '72.ci1.a1', '180.br1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8258, -1, 8267, -1, 6154, -1, 8245, -1], 'generators': [5, 8023685, 3669120, 120, 50803200], 'label': '2880.hl.36.br1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536335
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1.a1', '18.a1.a1'], 'contains': ['72.br1.a1', '72.bt1.a1', '72.bu1.a1', '72.bz1.a1', '72.cb1.a1', '72.ch1.a1', '72.cj1.a1', '180.bs1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9494, -1, 9128, -1, 7429, -1, 8943, -1], 'generators': [8023694, 5, 3669120, 120, 50803200], 'label': '2880.hl.36.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536336
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a1', '18.a1.a1'], 'contains': ['72.bx1.a1', '72.by1.a1', '72.cb1.a1', '72.cc1.a1', '72.cf1.a1', '72.cg1.a1', '72.cj1.a1', '180.bt1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8708, -1, 8572, -1, 6903, -1, 8860, -1], 'generators': [136, 5, 8023685, 3669120, 50803200], 'label': '2880.hl.36.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536337
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.t1.a1', '12.v1.a1', '12.x1.a1', '12.z1.a1', '12.ba1.a1', '12.be1.a1', '12.bf1.a1', '18.h1.a1', '30.h1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8056, -1, 7487, -1, 7287, -1, 7155, -1], 'generators': [127, 3669960, 1456, 9, 8025134, 50803200, 16], 'label': '2880.hl.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536338
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '18.a1.a1'], 'contains': ['72.bx1.a1', '72.bz1.a1', '72.ca1.a1', '72.cd1.a1', '72.cf1.a1', '72.ch1.a1', '72.ci1.a1', '180.bu1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9336, -1, 8688, -1, 7133, -1, 8902, -1], 'generators': [136, 8023694, 5, 3669120, 50803200], 'label': '2880.hl.36.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536339
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '40.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '144.b1.a1', 'complements': ['72.bz1.a1', '72.by1.a1', '72.cb1.a1', '72.ca1.a1', '72.ch1.a1', '72.cg1.a1', '72.cj1.a1', '72.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['80.a1.a1', '120.a1.a1', '120.bm1.a1', '160.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [448, 7444, 200, 7470, 232, 2378, 301, 7606], 'generators': [11, 124, 23, 1456, 7], 'label': '2880.hl.40.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536340
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '40.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '48.d1.a1', 'complements': ['72.cl1.a1', '72.cf1.a1', '72.bu1.a1', '72.bw1.a1', '72.bs1.a1', '72.cd1.a1', '72.cc1.a1', '72.bt1.a1', '72.ce1.a1', '72.ch1.a1', '72.cg1.a1', '72.cj1.a1', '72.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.a1.a1', '20.d1.a1', '20.j1.a1'], 'contains': ['80.a1.a1', '120.b1.a1', '120.bq1.a1', '160.c1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [181, 8399, 170, 8427, 875, 1227, 72, 8769], 'generators': [11, 23, 1456, 5, 7], 'label': '2880.hl.40.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': ['8.c1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536341
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '40.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '144.b1.a1', 'complements': ['72.bw1.a1', '72.bu1.a1', '72.cf1.a1', '72.cl1.a1', '72.bs1.a1', '72.bt1.a1', '72.cc1.a1', '72.cd1.a1', '72.ce1.a1', '72.ca1.a1', '72.cb1.a1', '72.by1.a1', '72.bz1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '20.a1.a1', '20.e1.a1', '20.k1.a1'], 'contains': ['80.a1.a1', '120.bt1.a1', '120.bu1.a1', '120.bv1.a1', '160.e1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [335, 7922, 259, 7948, 521, 1771, 270, 8229], 'generators': [11, 23, 122, 1456, 7], 'label': '2880.hl.40.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': ['8.e1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536342
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.b1.a1', '20.d1.a1', '20.e1.a1', '20.f1.a1', '20.g1.a1', '20.h1.a1', '20.i1.a1'], 'contains': ['80.a1.a1', '120.bn1.a1', '120.bo1.a1', '120.bp1.a1', '160.b1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4159, -1, 4173, -1, 4085, -1, 1044, -1], 'generators': [11, 23, 3669967, 1456, 7], 'label': '2880.hl.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536343
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '20.b1.a1', '20.j1.a1', '20.k1.a1'], 'contains': ['80.a1.a1', '120.br1.a1', '120.bs1.a1', '160.d1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [307, -1, 304, -1, 278, -1, 16, -1], 'generators': [11, 23, 1456, 3669848, 7], 'label': '2880.hl.40.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536344
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '20.c1.a1', '20.d1.a1', '20.k1.a1'], 'contains': ['80.a1.a1', '120.bw1.a1', '120.bx1.a1', '160.f1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [518, -1, 333, -1, 551, -1, 198, -1], 'generators': [11, 23, 1456, 3669969, 7], 'label': '2880.hl.40.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536345
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '20.c1.a1', '20.e1.a1', '20.j1.a1'], 'contains': ['80.a1.a1', '120.by1.a1', '120.bz1.a1', '120.ca1.a1', '160.g1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [401, -1, 457, -1, 417, -1, 157, -1], 'generators': [11, 23, 1456, 3669850, 7], 'label': '2880.hl.40.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536346
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '10.a1.a1', '20.l1.a1'], 'contains': ['80.b1.a1', '80.c1.a1', '80.d1.a1', '80.e1.a1', '80.f1.a1', '80.k1.a1', '80.l1.a1', '120.cb1.a1', '120.ce1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2140, -1, 2715, -1, 1467, -1, 403, -1], 'generators': [124, 1440, 3669960, 5, 3], 'label': '2880.hl.40.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '40.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536347
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '40.i1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '10.b1.a1', '20.l1.a1'], 'contains': ['80.b1.a1', '80.g1.a1', '80.h1.a1', '120.cc1.a1', '120.cf1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5446, -1, 5505, -1, 5215, -1, 1875, -1], 'generators': [1440, 8025132, 3669960, 128, 12], 'label': '2880.hl.40.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '40.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536348
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1', '12.bt1.a1', '12.cc1.a1', '12.cd1.a1', '18.i1.a1', '24.cc1.a1', '30.i1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2137, -1, 1662, -1, 1205, -1, 1178, -1], 'generators': [11, 124, 23, 5, 3669143, 50803200, 7], 'label': '2880.hl.6.k1.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.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536349
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '40.j1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '10.c1.a1', '20.l1.a1'], 'contains': ['80.b1.a1', '80.i1.a1', '80.j1.a1', '120.cd1.a1', '120.ch1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6222, -1, 6305, -1, 5523, -1, 1684, -1], 'generators': [124, 1440, 3669960, 8025121, 3], 'label': '2880.hl.40.j1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '40.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536350
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '40.k1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '10.d1.a1', '20.l1.a1'], 'contains': ['80.e1.a1', '80.g1.a1', '80.i1.a1', '120.cl1.a1', '120.cp1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5750, -1, 5762, -1, 5567, -1, 1482, -1], 'generators': [11, 1440, 3669960, 5, 8025126], 'label': '2880.hl.40.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '40.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536351
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '40.l1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '10.e1.a1', '20.l1.a1'], 'contains': ['80.e1.a1', '80.h1.a1', '80.j1.a1', '120.cn1.a1', '120.cq1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5951, -1, 6031, -1, 5259, -1, 1573, -1], 'generators': [11, 1440, 3669960, 5, 8025261], 'label': '2880.hl.40.l1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '40.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536352
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '40.m1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '10.f1.a1', '20.l1.a1'], 'contains': ['80.f1.a1', '80.g1.a1', '80.j1.a1', '120.cv1.a1', '120.cz1.a1', '120.db1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5891, -1, 5888, -1, 5720, -1, 1749, -1], 'generators': [1440, 8025132, 3669960, 8025242, 12], 'label': '2880.hl.40.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '40.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536353
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '40.n1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '10.g1.a1', '20.l1.a1'], 'contains': ['80.f1.a1', '80.h1.a1', '80.i1.a1', '120.cx1.a1', '120.da1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6053, -1, 6086, -1, 5431, -1, 1445, -1], 'generators': [1440, 3669960, 122, 12, 8025126], 'label': '2880.hl.40.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '40.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536354
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.a1.a1', '15.b1.a1'], 'contains': ['90.a1.a1', '90.b1.a1', '90.c1.a1', '90.d1.a1', '90.e1.a1', '90.f1.a1', '90.g1.a1', '90.h1.a1', '90.i1.a1', '90.j1.a1', '90.k1.a1', '90.l1.a1', '90.m1.a1', '90.n1.a1', '90.o1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7433, -1, 7561, -1, 8496, -1, 5468, -1], 'generators': [127, 23, 8023694, 5, 3669143, 7], 'label': '2880.hl.45.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536355
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '48.a1', 'aut_quo_index': 32, 'aut_stab_index': 1, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '48.a1.a1', 'complements': ['60.cf1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.e1.a1', '24.bt1.a1', '24.bv1.a1', '24.by1.a1', '24.bz1.a1'], 'contains': ['96.d1.a1', '144.a1.a1', '240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1069, 4806, 882, 4564, 1620, 4629, 2561, 5355], 'generators': [23, 1456, 50803200, 7], 'label': '2880.hl.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.e1.a1'], 'normal_contains': ['144.a1.a1', '192.a1.a1', '240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '48.35', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 183536371
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.p1.a1', '24.bb1.a1', '24.bh1.a1', '24.bn1.a1', '24.bq1.a1', '24.bz1.a1'], 'contains': ['96.d1.a1', '96.s1.a1', '144.l1.a1', '240.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3446, -1, 3513, -1, 3383, -1, 5004, -1], 'generators': [23, 1463, 3669842, 50803200], 'label': '2880.hl.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536356
    {'ambient': '2880.hl', 'aut_centralizer_order': 30, 'aut_label': '48.b1', 'aut_quo_index': 32, 'aut_stab_index': 1, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '96.a1.a1', 'complements': ['60.cj1.a1', '60.ci1.a1', '60.cg1.a1', '60.ch1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1', '24.d1.a1', '24.f1.a1', '24.br1.a1', '24.bu1.a1', '24.bw1.a1', '24.ca1.a1'], 'contains': ['144.a1.a1', '192.b1.a1', '240.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [824, 6290, 654, 6316, 223, 4046, 771, 5938], 'generators': [11, 23, 50803200, 7], 'label': '2880.hl.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.c1.a1', '24.d1.a1', '24.f1.a1'], 'normal_contains': ['144.a1.a1', '240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '16.10', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 183536357
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '120.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.g1.a1', '24.h1.a1', '24.cf1.a1', '24.cg1.a1', '24.ch1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '144.q1.a1', '240.u1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4093, 2358, 4137, 2229, 4780, 6856, 9022, 3366], 'generators': [1440, 3669960, 120, 50803200], 'label': '2880.hl.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['12.a1.a1', '24.g1.a1'], 'normal_contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536358
    {'ambient': '2880.hl', 'aut_centralizer_order': 72, 'aut_label': '48.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '40.b1.a1', 'complements': ['60.bh1.a1', '60.bi1.a1', '60.cd1.a1', '60.cc1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.g1.a1', '24.q1.a1', '24.cl1.a1', '24.cr1.a1', '24.cv1.a1'], 'contains': ['96.b1.a1', '144.b1.a1', '240.be1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8019, 983, 7479, 1108, 6806, 8352, 8707, 1632], 'generators': [8025120, 1440, 3669960, 50803200], 'label': '2880.hl.48.d1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['12.c1.a1', '24.g1.a1'], 'normal_contains': ['96.b1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536359
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.bm1.a1', '12.bx1.a1', '18.j1.a1', '24.cd1.a1', '30.j1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5282, -1, 5447, -1, 4852, -1, 2629, -1], 'generators': [11, 124, 23, 3669143, 8023692, 50803200, 7], 'label': '2880.hl.6.l1.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.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536360
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '48.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '120.b1.a1', 'complements': ['60.bh1.a1', '60.cc1.a1', '60.bi1.a1', '60.cd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.g1.a1', '24.t1.a1', '24.cn1.a1', '24.cs1.a1', '24.cx1.a1'], 'contains': ['96.b1.a1', '144.y1.a1', '240.bg1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8174, 1461, 8195, 1586, 6969, 7909, 8738, 2075], 'generators': [1440, 3669960, 8025240, 50803200], 'label': '2880.hl.48.e1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.e1.a1', 'normal_contained_in': ['12.d1.a1', '24.g1.a1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536361
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '96.j1.a1', '144.c1.a1', '240.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3911, -1, 3812, -1, 3914, -1, 5216, -1], 'generators': [127, 1447, 50803200, 7], 'label': '2880.hl.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.f1.a1', 'projective_image': '2880.hl', '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': '24.5'}
  • id: 183536362
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.h1.a1', '24.n1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1', '24.t1.a1', '24.u1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1', '24.y1.a1', '24.z1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.l1.a1', '144.d1.a1', '240.d1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6542, -1, 6575, -1, 6481, -1, 8635, -1], 'generators': [3669967, 1447, 50803200, 7], 'label': '2880.hl.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536363
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.n1.a1', '24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1', '24.bt1.a1'], 'contains': ['96.d1.a1', '96.h1.a1', '144.e1.a1', '240.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3971, -1, 4047, -1, 3662, -1, 4543, -1], 'generators': [1456, 5, 50803200, 16], 'label': '2880.hl.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.h1.a1', 'projective_image': '2880.hl', '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': '16.10'}
  • id: 183536364
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.o1.a1', '24.ba1.a1', '24.be1.a1', '24.bf1.a1', '24.bg1.a1', '24.bh1.a1'], 'contains': ['96.d1.a1', '96.j1.a1', '144.f1.a1', '240.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4036, -1, 3977, -1, 3981, -1, 4733, -1], 'generators': [136, 1447, 50803200, 7], 'label': '2880.hl.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 183536365
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.h1.a1', '24.bb1.a1', '24.be1.a1', '24.bi1.a1', '24.bj1.a1', '24.bk1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '96.r1.a1', '144.g1.a1', '240.g1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3815, -1, 3923, -1, 3948, -1, 5286, -1], 'generators': [1447, 3669840, 50803200, 7], 'label': '2880.hl.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536366
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.j1.a1', '24.bc1.a1', '24.be1.a1', '24.bl1.a1', '24.bm1.a1', '24.bn1.a1'], 'contains': ['96.d1.a1', '96.l1.a1', '144.h1.a1', '240.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4558, -1, 4515, -1, 4213, -1, 4773, -1], 'generators': [1447, 3669976, 50803200, 7], 'label': '2880.hl.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536367
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.p1.a1', '24.bf1.a1', '24.bi1.a1', '24.bl1.a1', '24.bo1.a1', '24.bv1.a1'], 'contains': ['96.d1.a1', '96.m1.a1', '144.i1.a1', '240.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3689, -1, 3554, -1, 3508, -1, 5080, -1], 'generators': [23, 122, 1463, 50803200], 'label': '2880.hl.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 183536368
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.n1.a1', '24.bg1.a1', '24.bi1.a1', '24.bm1.a1', '24.bp1.a1', '24.by1.a1'], 'contains': ['96.d1.a1', '96.p1.a1', '144.j1.a1', '240.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3552, -1, 3313, -1, 3548, -1, 5256, -1], 'generators': [1456, 3669965, 50803200, 16], 'label': '2880.hl.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536369
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.j1.a1', '24.o1.a1', '24.bd1.a1', '24.bo1.a1', '24.bp1.a1', '24.bq1.a1'], 'contains': ['96.d1.a1', '96.r1.a1', '144.k1.a1', '240.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4010, -1, 3949, -1, 4015, -1, 4485, -1], 'generators': [1447, 3669863, 50803200, 7], 'label': '2880.hl.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536370
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.bm1.a1', '12.by1.a1', '18.k1.a1', '24.ce1.a1', '30.k1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6340, -1, 6321, -1, 5279, -1, 2578, -1], 'generators': [11, 124, 23, 8023697, 3669143, 50803200, 7], 'label': '2880.hl.6.m1.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.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536372
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '48.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.r1.a1', '24.bf1.a1', '24.bj1.a1', '24.bm1.a1', '24.bq1.a1', '24.bt1.a1'], 'contains': ['96.d1.a1', '144.m1.a1', '240.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1168, -1, 969, -1, 1886, -1, 4600, -1], 'generators': [1456, 9, 50803200, 16], 'label': '2880.hl.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 183536373
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.35', 'aut_weyl_index': 60, 'centralizer': '144.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.u1.a1', '24.ba1.a1', '24.bk1.a1', '24.bn1.a1', '24.bp1.a1', '24.bv1.a1'], 'contains': ['96.d1.a1', '144.n1.a1', '240.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1642, -1, 1568, -1, 1993, -1, 4046, -1], 'generators': [23, 130, 1463, 50803200], 'label': '2880.hl.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 183536374
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.r1.a1', '24.bc1.a1', '24.bh1.a1', '24.bk1.a1', '24.bo1.a1', '24.by1.a1'], 'contains': ['96.d1.a1', '144.o1.a1', '240.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2101, -1, 1629, -1, 2316, -1, 3797, -1], 'generators': [1456, 3669969, 50803200, 16], 'label': '2880.hl.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536375
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.u1.a1', '24.bd1.a1', '24.bg1.a1', '24.bj1.a1', '24.bl1.a1', '24.bz1.a1'], 'contains': ['96.d1.a1', '144.p1.a1', '240.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1802, -1, 2274, -1, 2193, -1, 3958, -1], 'generators': [23, 1463, 3669850, 50803200], 'label': '2880.hl.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536376
    {'ambient': '2880.hl', 'aut_centralizer_order': 15, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.186', 'aut_weyl_index': 30, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.bs1.a1', '24.bx1.a1', '24.cb1.a1'], 'contains': ['144.a1.a1', '192.c1.a1', '240.q1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [855, -1, 707, -1, 327, -1, 1097, -1], 'generators': [23, 1460, 50803200, 7], 'label': '2880.hl.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '48.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 183536377
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '16.b1.a1', '24.cc1.a1', '24.cd1.a1', '24.ce1.a1'], 'contains': ['96.e1.a1', '96.f1.a1', '96.k1.a1', '144.q1.a1', '240.r1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2840, -1, 2344, -1, 784, -1, 2058, -1], 'generators': [124, 3669120, 3, 50803200], 'label': '2880.hl.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536378
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '16.c1.a1', '24.cc1.a1'], 'contains': ['96.e1.a1', '96.i1.a1', '96.n1.a1', '144.r1.a1', '240.s1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2990, -1, 2751, -1, 1285, -1, 998, -1], 'generators': [124, 5, 3, 50803200], 'label': '2880.hl.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536379
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1.a1', '16.d1.a1', '24.cc1.a1'], 'contains': ['96.e1.a1', '96.q1.a1', '96.t1.a1', '144.t1.a1', '240.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2602, -1, 1928, -1, 516, -1, 954, -1], 'generators': [3669125, 124, 3, 50803200], 'label': '2880.hl.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536380
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.i1.a1', '24.cf1.a1', '24.ci1.a1'], 'contains': ['96.a1.a1', '96.h1.a1', '96.m1.a1', '144.r1.a1', '240.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4268, -1, 4268, -1, 4434, -1, 9493, -1], 'generators': [1440, 5, 120, 50803200], 'label': '2880.hl.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536381
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.i1.a1', '12.m1.a1', '12.n1.a1', '12.o1.a1', '12.t1.a1', '12.bk1.a1', '12.bl1.a1', '12.bp1.a1', '12.bq1.a1', '12.br1.a1', '12.bs1.a1', '12.cb1.a1', '12.ce1.a1', '18.i1.a1', '30.l1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2484, -1, 2380, -1, 3054, -1, 3966, -1], 'generators': [127, 23, 3669967, 1456, 5, 50803200, 7], 'label': '2880.hl.6.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536382
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.j1.a1', '24.ci1.a1', '24.cj1.a1'], 'contains': ['96.a1.a1', '96.l1.a1', '96.r1.a1', '144.s1.a1', '240.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5703, -1, 5477, -1, 6087, -1, 9332, -1], 'generators': [1440, 3669967, 120, 50803200], 'label': '2880.hl.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536383
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.k1.a1', '24.cf1.a1', '24.ci1.a1'], 'contains': ['96.a1.a1', '96.p1.a1', '96.s1.a1', '144.t1.a1', '240.x1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4462, -1, 4411, -1, 4334, -1, 9570, -1], 'generators': [1440, 3669974, 120, 50803200], 'label': '2880.hl.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536384
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.n1.a1', '24.cf1.a1', '24.ck1.a1', '24.cl1.a1', '24.cm1.a1', '24.cn1.a1', '24.co1.a1'], 'contains': ['96.b1.a1', '96.h1.a1', '96.p1.a1', '144.u1.a1', '240.y1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5214, -1, 5377, -1, 5573, -1, 9606, -1], 'generators': [1440, 3669960, 5, 50803200], 'label': '2880.hl.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536385
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '16.e1.a1', '24.cc1.a1', '24.cp1.a1', '24.cq1.a1'], 'contains': ['96.f1.a1', '96.i1.a1', '96.q1.a1', '144.u1.a1', '240.z1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3288, -1, 3480, -1, 2501, -1, 1344, -1], 'generators': [11, 5, 3669120, 50803200], 'label': '2880.hl.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '48.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536386
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.o1.a1', '24.ck1.a1', '24.cr1.a1', '24.cs1.a1', '24.ct1.a1', '24.cu1.a1'], 'contains': ['96.b1.a1', '96.j1.a1', '96.r1.a1', '144.v1.a1', '240.ba1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6363, -1, 6624, -1, 6327, -1, 9186, -1], 'generators': [136, 1440, 3669960, 50803200], 'label': '2880.hl.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536387
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.p1.a1', '24.cf1.a1', '24.ck1.a1', '24.cv1.a1', '24.cw1.a1', '24.cx1.a1', '24.cy1.a1'], 'contains': ['96.b1.a1', '96.m1.a1', '96.s1.a1', '144.w1.a1', '240.bb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4869, -1, 5046, -1, 5213, -1, 9259, -1], 'generators': [1440, 3669960, 122, 50803200], 'label': '2880.hl.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536388
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '16.f1.a1', '24.cc1.a1', '24.cz1.a1', '24.da1.a1'], 'contains': ['96.f1.a1', '96.n1.a1', '96.t1.a1', '144.w1.a1', '240.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3071, -1, 3144, -1, 2465, -1, 1427, -1], 'generators': [122, 3669120, 12, 50803200], 'label': '2880.hl.48.be1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536389
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1.a1', '16.f1.a1', '24.db1.a1'], 'contains': ['96.g1.a1', '96.o1.a1', '96.u1.a1', '144.w1.a1', '240.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3365, -1, 3417, -1, 3193, -1, 1463, -1], 'generators': [122, 1443, 3669964, 50803200], 'label': '2880.hl.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.db1.a1', 'old_label': '48.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536390
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.s1.a1', '24.cg1.a1', '24.cm1.a1', '24.cs1.a1', '24.ct1.a1', '24.cw1.a1'], 'contains': ['96.b1.a1', '144.x1.a1', '240.bf1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9893, -1, 9413, -1, 7649, -1, 9223, -1], 'generators': [1440, 3669960, 8025136, 50803200], 'label': '2880.hl.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536391
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.w1.a1', '24.ch1.a1', '24.cl1.a1', '24.cm1.a1', '24.cu1.a1', '24.cx1.a1', '24.cy1.a1'], 'contains': ['96.b1.a1', '144.z1.a1', '240.bh1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9144, -1, 8866, -1, 7107, -1, 9101, -1], 'generators': [1440, 3669960, 8025126, 50803200], 'label': '2880.hl.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536392
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.k1.a1', '12.l1.a1', '12.w1.a1', '12.x1.a1', '12.bv1.a1', '12.bw1.a1', '18.k1.a1', '30.n1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6906, -1, 6949, -1, 6223, -1, 6361, -1], 'generators': [127, 23, 3669967, 1456, 8025137, 50803200, 7], 'label': '2880.hl.6.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536393
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.x1.a1', '24.cg1.a1', '24.co1.a1', '24.cr1.a1', '24.ct1.a1', '24.cy1.a1'], 'contains': ['96.b1.a1', '144.ba1.a1', '240.bi1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9404, -1, 9593, -1, 7715, -1, 9156, -1], 'generators': [8025256, 1440, 3669960, 50803200], 'label': '2880.hl.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536394
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.y1.a1', '24.ch1.a1', '24.cn1.a1', '24.co1.a1', '24.cu1.a1', '24.cv1.a1', '24.cw1.a1'], 'contains': ['96.b1.a1', '144.bb1.a1', '240.bj1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8680, -1, 8450, -1, 6944, -1, 9131, -1], 'generators': [1440, 3669960, 8025261, 50803200], 'label': '2880.hl.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536395
    {'ambient': '2880.hl', 'aut_centralizer_order': 18, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '16.g1.a1', '24.cd1.a1', '24.cp1.a1', '24.cz1.a1'], 'contains': ['96.f1.a1', '144.b1.a1', '240.bk1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5185, -1, 5423, -1, 5500, -1, 2179, -1], 'generators': [3669120, 8023692, 12, 50803200], 'label': '2880.hl.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '48.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536396
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1.a1', '16.h1.a1', '24.cd1.a1', '24.cq1.a1', '24.da1.a1'], 'contains': ['96.f1.a1', '144.y1.a1', '240.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5625, -1, 5688, -1, 5844, -1, 2240, -1], 'generators': [8025255, 3669120, 20, 50803200], 'label': '2880.hl.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536397
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '16.i1.a1', '24.ce1.a1', '24.cp1.a1', '24.da1.a1'], 'contains': ['96.f1.a1', '144.z1.a1', '240.bm1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6307, -1, 6403, -1, 6010, -1, 2088, -1], 'generators': [11, 3669120, 8023686, 50803200], 'label': '2880.hl.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '48.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536398
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '16.j1.a1', '24.ce1.a1', '24.cq1.a1', '24.cz1.a1'], 'contains': ['96.f1.a1', '144.bb1.a1', '240.bn1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6120, -1, 6190, -1, 5698, -1, 2210, -1], 'generators': [11, 3669120, 8025261, 50803200], 'label': '2880.hl.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536399
    {'ambient': '2880.hl', 'aut_centralizer_order': 9, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '16.g1.a1', '24.db1.a1'], 'contains': ['96.g1.a1', '144.b1.a1', '240.bo1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5514, -1, 5586, -1, 6373, -1, 2119, -1], 'generators': [8025132, 1452, 3669968, 50803200], 'label': '2880.hl.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '48.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536400
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '16.j1.a1', '24.db1.a1'], 'contains': ['96.g1.a1', '144.bb1.a1', '240.bp1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6182, -1, 6257, -1, 6440, -1, 2149, -1], 'generators': [3669979, 1451, 8025261, 50803200], 'label': '2880.hl.48.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.db1.a1', 'old_label': '48.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536401
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.ck1.a1', '24.dc1.a1'], 'contains': ['96.h1.a1', '96.j1.a1', '96.m1.a1', '144.bc1.a1', '240.bq1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5441, -1, 5186, -1, 5149, -1, 9683, -1], 'generators': [136, 1440, 5, 50803200], 'label': '2880.hl.48.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536402
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.bb1.a1', '24.cf1.a1', '24.dc1.a1'], 'contains': ['96.c1.a1', '96.h1.a1', '96.s1.a1', '144.bd1.a1', '240.br1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4526, -1, 4733, -1, 4364, -1, 9459, -1], 'generators': [1440, 5, 3669840, 50803200], 'label': '2880.hl.48.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536403
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '12.p1.a1', '12.q1.a1', '12.bc1.a1', '12.be1.a1', '12.br1.a1', '12.bv1.a1', '18.l1.a1', '30.o1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7182, -1, 7937, -1, 6668, -1, 5885, -1], 'generators': [23, 3669967, 1456, 5, 8025134, 50803200, 7], 'label': '2880.hl.6.p1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}
  • id: 183536404
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.ci1.a1', '24.dc1.a1'], 'contains': ['96.h1.a1', '96.l1.a1', '96.p1.a1', '144.be1.a1', '240.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5409, -1, 5226, -1, 5375, -1, 9942, -1], 'generators': [1440, 5, 3669976, 50803200], 'label': '2880.hl.48.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536405
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '24.ci1.a1', '24.ck1.a1'], 'contains': ['96.h1.a1', '96.r1.a1', '96.s1.a1', '144.bf1.a1', '240.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5120, -1, 5158, -1, 5183, -1, 9796, -1], 'generators': [1440, 5, 3669856, 50803200], 'label': '2880.hl.48.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536406
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1.a1', '16.k1.a1', '24.cc1.a1'], 'contains': ['96.i1.a1', '96.k1.a1', '96.t1.a1', '144.bd1.a1', '240.bu1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2934, -1, 2619, -1, 1071, -1, 714, -1], 'generators': [5, 3669844, 3, 50803200], 'label': '2880.hl.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536407
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.be1.a1', '24.dc1.a1', '24.dd1.a1'], 'contains': ['96.c1.a1', '96.j1.a1', '96.l1.a1', '144.bg1.a1', '240.bv1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5793, -1, 5506, -1, 6051, -1, 9296, -1], 'generators': [127, 1440, 3669967, 50803200], 'label': '2880.hl.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536408
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.o1.a1', '24.be1.a1'], 'contains': ['96.j1.a1', '96.l1.a1', '96.r1.a1', '144.bh1.a1', '240.bw1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5764, -1, 5306, -1, 5412, -1, 6314, -1], 'generators': [1440, 143, 3669967, 50803200], 'label': '2880.hl.48.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536409
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.ck1.a1', '24.dc1.a1'], 'contains': ['96.j1.a1', '96.p1.a1', '96.s1.a1', '144.bi1.a1', '240.bx1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5088, -1, 4840, -1, 4936, -1, 9723, -1], 'generators': [136, 1440, 3669974, 50803200], 'label': '2880.hl.48.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536410
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '16.l1.a1', '24.cc1.a1'], 'contains': ['96.k1.a1', '96.n1.a1', '96.q1.a1', '144.bj1.a1', '240.by1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2472, -1, 2035, -1, 982, -1, 837, -1], 'generators': [3669125, 3669844, 3, 50803200], 'label': '2880.hl.48.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '48.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536411
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.bi1.a1', '24.cf1.a1', '24.dc1.a1'], 'contains': ['96.c1.a1', '96.m1.a1', '96.p1.a1', '144.bj1.a1', '240.bz1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4187, -1, 4349, -1, 4394, -1, 9533, -1], 'generators': [1440, 3669840, 3669974, 50803200], 'label': '2880.hl.48.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536412
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.ci1.a1', '24.dc1.a1'], 'contains': ['96.l1.a1', '96.m1.a1', '96.s1.a1', '144.bk1.a1', '240.ca1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4791, -1, 4869, -1, 4900, -1, 9905, -1], 'generators': [1440, 122, 3669983, 50803200], 'label': '2880.hl.48.ca1.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': '48.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536413
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '240.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '24.cj1.a1', '24.dd1.a1'], 'contains': ['96.l1.a1', '144.bl1.a1', '240.cb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6494, -1, 6501, -1, 6697, -1, 9369, -1], 'generators': [1440, 3669967, 8025137, 50803200], 'label': '2880.hl.48.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536414
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['1440.d1.a1', '1440.h1.a1', '1440.i1.a1', '1440.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '6.m1.a1', '6.o1.a1', '8.j1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6293, 4518, 6318, 3794, 5491, 5655, 2450, 4345], 'generators': [11, 124, 23, 3669967, 1456, 8025137, 50803200, 7], 'label': '2880.hl.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '2880.hl', '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': '2880.hl'}
  • id: 183536415
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.r1.a1', '12.s1.a1', '12.bf1.a1', '12.bg1.a1', '12.br1.a1', '12.bw1.a1', '18.m1.a1', '30.p1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7944, -1, 7077, -1, 7377, -1, 6314, -1], 'generators': [23, 3669967, 1456, 5, 8025254, 50803200, 7], 'label': '2880.hl.6.q1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536416
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '24.cj1.a1', '24.dd1.a1'], 'contains': ['96.l1.a1', '144.bm1.a1', '240.cc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6627, -1, 6546, -1, 6595, -1, 9435, -1], 'generators': [1440, 3669983, 8025253, 50803200], 'label': '2880.hl.48.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536417
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '24.ci1.a1', '24.ck1.a1'], 'contains': ['96.m1.a1', '96.p1.a1', '96.r1.a1', '144.bn1.a1', '240.cd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5050, -1, 4614, -1, 4972, -1, 9826, -1], 'generators': [1440, 3669856, 3669974, 50803200], 'label': '2880.hl.48.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536418
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '30.a1.a1', '30.b1.a1', '30.l1.a1'], 'contains': ['120.c1.a1', '120.d1.a1', '120.f1.a1', '120.i1.a1', '120.k1.a1', '120.w1.a1', '120.bd1.a1', '120.ce1.a1', '120.ci1.a1', '120.ck1.a1', '120.dc1.a1', '180.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4406, -1, 5018, -1, 4467, -1, 6622, -1], 'generators': [3669960, 1456, 5, 120, 16], 'label': '2880.hl.60.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536419
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '30.a1.a1', '30.c1.a1', '30.m1.a1'], 'contains': ['120.c1.a1', '120.l1.a1', '120.o1.a1', '120.cf1.a1', '120.cg1.a1', '120.cr1.a1', '120.cs1.a1', '180.b1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8400, -1, 8946, -1, 9763, -1, 6833, -1], 'generators': [127, 8025127, 3669967, 1447, 7], 'label': '2880.hl.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536420
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '30.c1.a1', '30.d1.a1', '30.l1.a1'], 'contains': ['120.c1.a1', '120.g1.a1', '120.h1.a1', '120.m1.a1', '120.p1.a1', '120.be1.a1', '120.bf1.a1', '180.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [955, -1, 1536, -1, 2484, -1, 4689, -1], 'generators': [3669960, 1456, 9, 120, 16], 'label': '2880.hl.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536421
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '30.b1.a1', '30.d1.a1', '30.m1.a1'], 'contains': ['120.c1.a1', '120.n1.a1', '120.s1.a1', '120.cg1.a1', '120.ct1.a1', '180.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9988, -1, 9988, -1, 9974, -1, 7128, -1], 'generators': [127, 3669967, 8025136, 1447, 7], 'label': '2880.hl.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536422
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '30.b1.a1', '30.c1.a1', '30.n1.a1'], 'contains': ['120.c1.a1', '120.q1.a1', '120.u1.a1', '120.cj1.a1', '120.dd1.a1', '180.e1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6703, -1, 6827, -1, 8063, -1, 7355, -1], 'generators': [127, 3669967, 1447, 8025137, 7], 'label': '2880.hl.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536423
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '30.a1.a1', '30.d1.a1', '30.n1.a1'], 'contains': ['120.c1.a1', '120.r1.a1', '120.t1.a1', '120.ch1.a1', '120.cu1.a1', '180.f1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8870, -1, 9582, -1, 9176, -1, 6360, -1], 'generators': [127, 3669967, 1447, 8025126, 7], 'label': '2880.hl.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536424
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '30.l1.a1'], 'contains': ['120.d1.a1', '120.e1.a1', '120.h1.a1', '120.x1.a1', '120.y1.a1', '120.bg1.a1', '120.bj1.a1', '180.g1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3340, -1, 3253, -1, 3390, -1, 3342, -1], 'generators': [3669967, 1456, 5, 120, 16], 'label': '2880.hl.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536425
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '30.l1.a1'], 'contains': ['120.e1.a1', '120.f1.a1', '120.g1.a1', '120.bh1.a1', '120.bi1.a1', '120.bk1.a1', '120.bl1.a1', '180.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2332, -1, 2890, -1, 3015, -1, 3415, -1], 'generators': [3669967, 1456, 9, 120, 16], 'label': '2880.hl.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536426
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.bx1.a1', '12.by1.a1', '18.m1.a1', '24.cq1.a1', '30.r1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5753, -1, 6113, -1, 5041, -1, 2538, -1], 'generators': [11, 23, 5, 8025253, 3669143, 50803200, 7], 'label': '2880.hl.6.r1.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.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536427
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '30.e1.a1', '30.f1.a1', '30.l1.a1'], 'contains': ['120.i1.a1', '120.j1.a1', '120.p1.a1', '120.v1.a1', '120.y1.a1', '120.bb1.a1', '120.bk1.a1', '180.i1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3761, -1, 3577, -1, 3669, -1, 4740, -1], 'generators': [127, 3669960, 1456, 5, 16], 'label': '2880.hl.60.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536428
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '30.a1.a1', '30.e1.a1', '30.o1.a1'], 'contains': ['120.i1.a1', '120.l1.a1', '120.r1.a1', '120.cl1.a1', '120.cm1.a1', '180.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7851, -1, 8260, -1, 9319, -1, 6526, -1], 'generators': [3669960, 1456, 5, 8025134, 16], 'label': '2880.hl.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536429
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '30.b1.a1', '30.f1.a1', '30.o1.a1'], 'contains': ['120.i1.a1', '120.n1.a1', '120.q1.a1', '180.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6876, -1, 7319, -1, 8725, -1, 6887, -1], 'generators': [3669960, 1456, 5, 8025138, 16], 'label': '2880.hl.60.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536430
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '30.a1.a1', '30.f1.a1', '30.p1.a1'], 'contains': ['120.i1.a1', '120.o1.a1', '120.t1.a1', '120.cn1.a1', '120.co1.a1', '180.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9262, -1, 9523, -1, 9368, -1, 6576, -1], 'generators': [3669960, 1456, 5, 8025254, 16], 'label': '2880.hl.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536431
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '30.b1.a1', '30.e1.a1', '30.p1.a1'], 'contains': ['120.i1.a1', '120.s1.a1', '120.u1.a1', '180.m1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7301, -1, 7045, -1, 8330, -1, 6793, -1], 'generators': [3669960, 1456, 5, 8025258, 16], 'label': '2880.hl.60.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536432
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '30.g1.a1', '30.h1.a1', '30.l1.a1'], 'contains': ['120.j1.a1', '120.k1.a1', '120.m1.a1', '120.ba1.a1', '120.bc1.a1', '120.bj1.a1', '120.bl1.a1', '180.n1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2283, -1, 3112, -1, 3543, -1, 4785, -1], 'generators': [127, 3669960, 1456, 9, 16], 'label': '2880.hl.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536433
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '30.e1.a1', '30.g1.a1', '30.m1.a1'], 'contains': ['120.j1.a1', '120.l1.a1', '120.s1.a1', '120.cr1.a1', '120.ct1.a1', '180.o1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8334, -1, 8344, -1, 9862, -1, 7016, -1], 'generators': [136, 8025127, 3669967, 1447, 7], 'label': '2880.hl.60.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536434
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.p1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '30.f1.a1', '30.h1.a1', '30.m1.a1'], 'contains': ['120.j1.a1', '120.n1.a1', '120.o1.a1', '120.cs1.a1', '120.ct1.a1', '180.p1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9875, -1, 9804, -1, 9918, -1, 6473, -1], 'generators': [136, 3669967, 8025136, 1447, 7], 'label': '2880.hl.60.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536435
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.q1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '30.f1.a1', '30.g1.a1', '30.n1.a1'], 'contains': ['120.j1.a1', '120.q1.a1', '120.t1.a1', '180.q1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6914, -1, 7288, -1, 8534, -1, 6277, -1], 'generators': [136, 3669967, 1447, 8025137, 7], 'label': '2880.hl.60.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536436
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.r1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '30.e1.a1', '30.h1.a1', '30.n1.a1'], 'contains': ['120.j1.a1', '120.r1.a1', '120.u1.a1', '180.r1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7198, -1, 7101, -1, 8305, -1, 6013, -1], 'generators': [136, 3669967, 1447, 8025126, 7], 'label': '2880.hl.60.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536437
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '12.y1.a1', '12.z1.a1', '12.bd1.a1', '12.bh1.a1', '12.bs1.a1', '12.bw1.a1', '18.n1.a1', '30.s1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7813, -1, 7287, -1, 6589, -1, 6269, -1], 'generators': [23, 3669967, 8025136, 1456, 8025253, 50803200, 7], 'label': '2880.hl.6.s1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536438
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.s1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '30.a1.a1', '30.g1.a1', '30.s1.a1'], 'contains': ['120.k1.a1', '120.l1.a1', '120.t1.a1', '120.cv1.a1', '120.cw1.a1', '180.s1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8241, -1, 8004, -1, 9071, -1, 6728, -1], 'generators': [23, 3669960, 8025143, 1463, 8025261], 'label': '2880.hl.60.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536439
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.t1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '30.b1.a1', '30.h1.a1', '30.s1.a1'], 'contains': ['120.k1.a1', '120.n1.a1', '120.u1.a1', '180.t1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7336, -1, 7072, -1, 8280, -1, 6768, -1], 'generators': [23, 3669960, 8025136, 1463, 8025253], 'label': '2880.hl.60.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536440
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.u1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '30.a1.a1', '30.h1.a1', '30.t1.a1'], 'contains': ['120.k1.a1', '120.o1.a1', '120.r1.a1', '120.cx1.a1', '120.cy1.a1', '180.u1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9219, -1, 9636, -1, 9534, -1, 6416, -1], 'generators': [23, 3669960, 122, 1463, 8025141], 'label': '2880.hl.60.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536441
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.v1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '30.b1.a1', '30.g1.a1', '30.t1.a1'], 'contains': ['120.k1.a1', '120.q1.a1', '120.s1.a1', '180.v1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6942, -1, 7426, -1, 8807, -1, 6975, -1], 'generators': [23, 3669960, 122, 1463, 8025133], 'label': '2880.hl.60.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.v1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536442
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '60.w1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '30.c1.a1', '30.g1.a1', '30.o1.a1'], 'contains': ['120.l1.a1', '120.m1.a1', '120.q1.a1', '180.w1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7247, -1, 7633, -1, 8605, -1, 6243, -1], 'generators': [3669960, 1456, 9, 8025138, 16], 'label': '2880.hl.60.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536443
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '30.c1.a1', '30.e1.a1', '30.s1.a1'], 'contains': ['120.l1.a1', '120.p1.a1', '120.u1.a1', '180.x1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7617, -1, 7398, -1, 8201, -1, 6085, -1], 'generators': [23, 3669960, 8025143, 1463, 8025253], 'label': '2880.hl.60.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536444
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '60.y1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '30.d1.a1', '30.h1.a1', '30.o1.a1'], 'contains': ['120.m1.a1', '120.n1.a1', '120.r1.a1', '180.y1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9940, -1, 9939, -1, 9272, -1, 5805, -1], 'generators': [3669960, 1456, 9, 8025134, 16], 'label': '2880.hl.60.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536445
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.z1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '30.c1.a1', '30.h1.a1', '30.p1.a1'], 'contains': ['120.m1.a1', '120.o1.a1', '120.u1.a1', '180.z1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7693, -1, 7162, -1, 8246, -1, 5978, -1], 'generators': [3669960, 1456, 8025258, 9, 16], 'label': '2880.hl.60.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.z1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536446
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.ba1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '30.d1.a1', '30.g1.a1', '30.p1.a1'], 'contains': ['120.m1.a1', '120.s1.a1', '120.t1.a1', '180.ba1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8660, -1, 9453, -1, 9027, -1, 6205, -1], 'generators': [3669960, 1456, 8025254, 9, 16], 'label': '2880.hl.60.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536447
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bb1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '30.d1.a1', '30.f1.a1', '30.s1.a1'], 'contains': ['120.n1.a1', '120.p1.a1', '120.t1.a1', '180.bb1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8605, -1, 9475, -1, 8998, -1, 5943, -1], 'generators': [23, 3669960, 8025136, 1463, 8025261], 'label': '2880.hl.60.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536448
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.ba1.a1', '12.bb1.a1', '12.bi1.a1', '12.bj1.a1', '12.bs1.a1', '12.bv1.a1', '18.o1.a1', '30.t1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7052, -1, 8110, -1, 7476, -1, 5940, -1], 'generators': [8025133, 23, 7, 1456, 122, 3669967, 50803200], 'label': '2880.hl.6.t1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536449
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.bc1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '30.c1.a1', '30.f1.a1', '30.t1.a1'], 'contains': ['120.o1.a1', '120.p1.a1', '120.q1.a1', '180.bc1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7038, -1, 7767, -1, 8773, -1, 6130, -1], 'generators': [23, 3669960, 130, 1463, 8025133], 'label': '2880.hl.60.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536450
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bd1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '30.d1.a1', '30.e1.a1', '30.t1.a1'], 'contains': ['120.p1.a1', '120.r1.a1', '120.s1.a1', '180.bd1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9704, -1, 9717, -1, 9681, -1, 5840, -1], 'generators': [23, 3669960, 130, 1463, 8025141], 'label': '2880.hl.60.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536451
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.be1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '30.l1.a1'], 'contains': ['120.v1.a1', '120.w1.a1', '120.x1.a1', '120.z1.a1', '120.bc1.a1', '120.bf1.a1', '120.bi1.a1', '180.be1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3283, -1, 3642, -1, 3264, -1, 3378, -1], 'generators': [127, 3669967, 1456, 5, 16], 'label': '2880.hl.60.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.be1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536452
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bf1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '30.l1.a1'], 'contains': ['120.z1.a1', '120.ba1.a1', '120.bb1.a1', '120.bd1.a1', '120.be1.a1', '120.bg1.a1', '120.bh1.a1', '180.bf1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2382, -1, 2518, -1, 3127, -1, 3493, -1], 'generators': [127, 3669967, 1456, 9, 16], 'label': '2880.hl.60.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536453
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bg1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '20.b1.a1', '30.i1.a1', '30.j1.a1', '30.k1.a1'], 'contains': ['120.bm1.a1', '120.bo1.a1', '120.br1.a1', '180.bg1.a1', '240.r1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [539, -1, 535, -1, 590, -1, 1289, -1], 'generators': [11, 124, 23, 3669143, 7], 'label': '2880.hl.60.bg1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536454
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '60.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '20.a1.a1', '30.i1.a1'], 'contains': ['120.b1.a1', '120.bm1.a1', '120.bu1.a1', '180.bh1.a1', '240.s1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [216, -1, 130, -1, 447, -1, 790, -1], 'generators': [11, 124, 23, 5, 7], 'label': '2880.hl.60.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536455
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bi1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1.a1', '20.c1.a1', '30.i1.a1'], 'contains': ['120.bm1.a1', '120.bx1.a1', '120.bz1.a1', '180.bi1.a1', '240.t1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [339, -1, 304, -1, 314, -1, 729, -1], 'generators': [3669138, 11, 124, 23, 7], 'label': '2880.hl.60.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536456
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.bj1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.b1.a1', '30.l1.a1', '30.m1.a1', '30.n1.a1'], 'contains': ['120.a1.a1', '120.c1.a1', '120.e1.a1', '120.j1.a1', '120.z1.a1', '120.bn1.a1', '120.bs1.a1', '180.bg1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4891, -1, 4649, -1, 4269, -1, 3454, -1], 'generators': [127, 23, 3669967, 1456, 7], 'label': '2880.hl.60.bj1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536457
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '60.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '20.a1.a1', '30.l1.a1'], 'contains': ['120.a1.a1', '120.d1.a1', '120.g1.a1', '120.v1.a1', '120.ba1.a1', '120.bq1.a1', '120.bt1.a1', '180.bh1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [791, -1, 1077, -1, 2359, -1, 2739, -1], 'generators': [127, 23, 1456, 5, 7], 'label': '2880.hl.60.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536458
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bl1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.a1', '20.c1.a1', '30.l1.a1'], 'contains': ['120.a1.a1', '120.f1.a1', '120.h1.a1', '120.bb1.a1', '120.bc1.a1', '120.bw1.a1', '120.by1.a1', '180.bi1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1982, -1, 2103, -1, 2395, -1, 2703, -1], 'generators': [127, 23, 1456, 3669969, 7], 'label': '2880.hl.60.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536459
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.bt1.a1', '12.by1.a1', '18.n1.a1', '24.cz1.a1', '30.u1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5487, -1, 5525, -1, 4792, -1, 2314, -1], 'generators': [11, 23, 8025253, 3669143, 8023692, 50803200, 7], 'label': '2880.hl.6.u1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536460
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '60.bm1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '20.d1.a1', '30.l1.a1', '30.o1.a1', '30.p1.a1'], 'contains': ['120.i1.a1', '120.m1.a1', '120.x1.a1', '120.bh1.a1', '120.bn1.a1', '120.bq1.a1', '120.bw1.a1', '180.bj1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3148, -1, 1357, -1, 3503, -1, 3262, -1], 'generators': [23, 3669967, 1456, 5, 7], 'label': '2880.hl.60.bm1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536461
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '60.bn1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.d1.a1', '30.i1.a1', '30.q1.a1', '30.r1.a1'], 'contains': ['120.b1.a1', '120.bo1.a1', '120.bx1.a1', '180.bj1.a1', '240.z1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3072, -1, 567, -1, 2180, -1, 1008, -1], 'generators': [11, 23, 5, 3669143, 7], 'label': '2880.hl.60.bn1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536462
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bo1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '20.e1.a1', '30.l1.a1', '30.s1.a1', '30.t1.a1'], 'contains': ['120.k1.a1', '120.p1.a1', '120.bg1.a1', '120.bi1.a1', '120.bn1.a1', '120.bt1.a1', '120.by1.a1', '180.bk1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1214, -1, 2394, -1, 2821, -1, 3222, -1], 'generators': [23, 3669967, 122, 1456, 7], 'label': '2880.hl.60.bo1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536463
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bp1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '20.e1.a1', '30.i1.a1', '30.u1.a1', '30.v1.a1'], 'contains': ['120.bo1.a1', '120.bu1.a1', '120.bz1.a1', '180.bk1.a1', '240.bc1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [570, -1, 1710, -1, 1371, -1, 1137, -1], 'generators': [11, 23, 122, 3669143, 7], 'label': '2880.hl.60.bp1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536464
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '60.bq1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1.a1', '20.e1.a1', '30.w1.a1'], 'contains': ['120.bp1.a1', '120.bv1.a1', '120.ca1.a1', '180.bk1.a1', '240.bd1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [599, -1, 1747, -1, 1693, -1, 1230, -1], 'generators': [23, 122, 1460, 3669964, 7], 'label': '2880.hl.60.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.w1.a1', 'old_label': '60.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536465
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '60.br1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '60.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.f1.a1', '30.m1.a1', '30.o1.a1', '30.s1.a1'], 'contains': ['120.l1.a1', '120.n1.a1', '120.bn1.a1', '180.bl1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7771, -1, 7830, -1, 9124, -1, 4580, -1], 'generators': [23, 3669967, 8025136, 1456, 7], 'label': '2880.hl.60.br1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536466
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.bs1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.g1.a1', '30.m1.a1', '30.p1.a1', '30.t1.a1'], 'contains': ['120.o1.a1', '120.s1.a1', '120.bn1.a1', '180.bm1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9571, -1, 9678, -1, 9643, -1, 4968, -1], 'generators': [8025256, 23, 3669967, 1456, 7], 'label': '2880.hl.60.bs1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536467
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '60.bt1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1.a1', '20.h1.a1', '30.n1.a1', '30.o1.a1', '30.t1.a1'], 'contains': ['120.q1.a1', '120.r1.a1', '120.bn1.a1', '180.bn1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6828, -1, 7209, -1, 8446, -1, 4530, -1], 'generators': [23, 3669967, 1456, 8025137, 7], 'label': '2880.hl.60.bt1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536468
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bu1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '20.i1.a1', '30.n1.a1', '30.p1.a1', '30.s1.a1'], 'contains': ['120.t1.a1', '120.u1.a1', '120.bn1.a1', '180.bo1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7128, -1, 6976, -1, 8023, -1, 5056, -1], 'generators': [23, 3669967, 1456, 8025253, 7], 'label': '2880.hl.60.bu1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536469
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '60.bv1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.f1.a1', '30.j1.a1', '30.q1.a1', '30.u1.a1'], 'contains': ['120.bo1.a1', '180.bl1.a1', '240.bk1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5339, -1, 5547, -1, 4619, -1, 1824, -1], 'generators': [11, 23, 3669143, 8023692, 7], 'label': '2880.hl.60.bv1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536470
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.bt1.a1', '12.bx1.a1', '18.o1.a1', '24.da1.a1', '30.v1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6011, -1, 6180, -1, 5320, -1, 2178, -1], 'generators': [11, 23, 8023697, 122, 3669143, 50803200, 7], 'label': '2880.hl.6.v1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536471
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.bw1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1.a1', '20.g1.a1', '30.j1.a1', '30.r1.a1', '30.v1.a1'], 'contains': ['120.bo1.a1', '180.bm1.a1', '240.bl1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5659, -1, 5795, -1, 5121, -1, 1532, -1], 'generators': [11, 23, 8025255, 3669143, 7], 'label': '2880.hl.60.bw1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536472
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '60.bx1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '20.h1.a1', '30.k1.a1', '30.q1.a1', '30.v1.a1'], 'contains': ['120.bo1.a1', '180.bn1.a1', '240.bm1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6455, -1, 6413, -1, 5394, -1, 1408, -1], 'generators': [11, 23, 8023697, 3669143, 7], 'label': '2880.hl.60.bx1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536473
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.by1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '20.i1.a1', '30.k1.a1', '30.r1.a1', '30.u1.a1'], 'contains': ['120.bo1.a1', '180.bo1.a1', '240.bn1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6254, -1, 6307, -1, 4932, -1, 1784, -1], 'generators': [11, 23, 8025253, 3669143, 7], 'label': '2880.hl.60.by1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.by1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536474
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '60.bz1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '20.f1.a1', '30.w1.a1'], 'contains': ['120.bp1.a1', '180.bl1.a1', '240.bo1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5581, -1, 5733, -1, 5800, -1, 1925, -1], 'generators': [23, 8025132, 1460, 3669964, 7], 'label': '2880.hl.60.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.f1.a1', 'old_label': '60.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536475
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '60.ca1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '20.i1.a1', '30.w1.a1'], 'contains': ['120.bp1.a1', '180.bo1.a1', '240.bp1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6316, -1, 6352, -1, 5887, -1, 2002, -1], 'generators': [23, 1460, 3669964, 8025253, 7], 'label': '2880.hl.60.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.w1.a1', 'old_label': '60.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536476
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.cb1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '20.j1.a1', '30.l1.a1'], 'contains': ['120.w1.a1', '120.y1.a1', '120.be1.a1', '120.bl1.a1', '120.bq1.a1', '120.bs1.a1', '120.by1.a1', '180.bp1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [876, -1, 2920, -1, 1906, -1, 2630, -1], 'generators': [23, 1456, 5, 3669863, 7], 'label': '2880.hl.60.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536477
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.cc1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1.a1', '20.j1.a1', '30.i1.a1'], 'contains': ['120.b1.a1', '120.br1.a1', '120.bz1.a1', '180.bp1.a1', '240.bu1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [168, -1, 400, -1, 350, -1, 539, -1], 'generators': [11, 23, 5, 3669848, 7], 'label': '2880.hl.60.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536478
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.cd1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '20.k1.a1', '30.i1.a1'], 'contains': ['120.br1.a1', '120.bu1.a1', '120.bx1.a1', '180.bq1.a1', '240.by1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [301, -1, 249, -1, 386, -1, 682, -1], 'generators': [3669138, 11, 23, 3669848, 7], 'label': '2880.hl.60.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536479
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.ce1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '20.k1.a1', '30.l1.a1'], 'contains': ['120.bd1.a1', '120.bf1.a1', '120.bj1.a1', '120.bk1.a1', '120.bs1.a1', '120.bt1.a1', '120.bw1.a1', '180.bq1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1409, -1, 1581, -1, 1942, -1, 2666, -1], 'generators': [23, 1456, 3669863, 3669969, 7], 'label': '2880.hl.60.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.ce1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536480
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '60.cf1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.a1', '15.a1.a1', '20.l1.a1'], 'contains': ['120.cb1.a1', '120.cc1.a1', '120.cd1.a1', '120.cp1.a1', '120.cq1.a1', '120.cz1.a1', '120.da1.a1', '180.br1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6075, -1, 6121, -1, 5054, -1, 1634, -1], 'generators': [8023681, 124, 5, 3669120, 3], 'label': '2880.hl.60.cf1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '60.cf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536481
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['12.bu1.a1', '12.bz1.a1', '12.ca1.a1', '18.n1.a1', '24.db1.a1', '30.w1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5972, -1, 5787, -1, 5876, -1, 2214, -1], 'generators': [23, 8025132, 1460, 3669964, 8025253, 50803200, 7], 'label': '2880.hl.6.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '6.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536482
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.cg1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1.a1', '20.l1.a1', '30.a1.a1'], 'contains': ['120.ce1.a1', '120.cf1.a1', '120.ch1.a1', '120.cl1.a1', '120.cn1.a1', '120.cv1.a1', '120.cx1.a1', '180.br1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8146, -1, 8182, -1, 8958, -1, 7072, -1], 'generators': [1440, 3669960, 5, 8025125, 120], 'label': '2880.hl.60.cg1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.cg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536483
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.ch1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1.a1', '30.a1.a1'], 'contains': ['120.ce1.a1', '120.cg1.a1', '120.ch1.a1', '120.cm1.a1', '120.co1.a1', '120.cw1.a1', '120.cy1.a1', '180.bs1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9822, -1, 9882, -1, 9590, -1, 7600, -1], 'generators': [1440, 3669960, 5, 8025134, 120], 'label': '2880.hl.60.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.ch1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536484
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.ci1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a1', '30.a1.a1'], 'contains': ['120.ck1.a1', '120.cl1.a1', '120.co1.a1', '120.cr1.a1', '120.cu1.a1', '120.cv1.a1', '120.cy1.a1', '180.bt1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8548, -1, 9400, -1, 9422, -1, 7544, -1], 'generators': [136, 1440, 3669960, 5, 8025125], 'label': '2880.hl.60.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.ci1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536485
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '60.cj1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '30.a1.a1'], 'contains': ['120.ck1.a1', '120.cm1.a1', '120.cn1.a1', '120.cs1.a1', '120.cu1.a1', '120.cw1.a1', '120.cx1.a1', '180.bu1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9760, -1, 9750, -1, 9478, -1, 7657, -1], 'generators': [136, 1440, 3669960, 5, 8025134], 'label': '2880.hl.60.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.cj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536486
    {'ambient': '2880.hl', 'aut_centralizer_order': 45, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.c1.a1', '320.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2731, -1, 2199, -1, 1003, -1, 589, -1], 'generators': [11, 1440, 50803200], 'label': '2880.hl.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 183536487
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '24.bs1.a1', '36.a1.a1', '36.bh1.a1', '36.bk1.a1', '36.bl1.a1', '36.bm1.a1', '36.bn1.a1', '36.bo1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.h1.a1', '360.bl1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4935, 3140, 4735, 3240, 4612, 6281, 4813, 3942], 'generators': [23, 3669143, 50803200, 7], 'label': '2880.hl.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.b1.a1', '24.c1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536488
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.b1.a1', '36.c1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '36.bh1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.g1.a1', '144.q1.a1', '144.s1.a1', '144.v1.a1', '144.bg1.a1', '360.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6032, -1, 5826, -1, 6172, -1, 8185, -1], 'generators': [127, 3669120, 50803200, 7], 'label': '2880.hl.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536489
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.b1.a1', '36.h1.a1', '36.bi1.a1'], 'contains': ['144.c1.a1', '144.e1.a1', '144.i1.a1', '144.r1.a1', '144.bc1.a1', '360.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3622, -1, 3432, -1, 3462, -1, 5127, -1], 'generators': [5, 120, 50803200, 16], 'label': '2880.hl.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '2880.hl', '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': '8.2'}
  • id: 183536490
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.h1.a1', '36.i1.a1', '36.bh1.a1'], 'contains': ['144.c1.a1', '144.h1.a1', '144.k1.a1', '144.s1.a1', '144.bh1.a1', '360.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4729, -1, 4528, -1, 4174, -1, 4971, -1], 'generators': [127, 3669143, 50803200, 7], 'label': '2880.hl.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536491
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.b1.a1', '36.i1.a1', '36.bj1.a1'], 'contains': ['144.c1.a1', '144.j1.a1', '144.l1.a1', '144.t1.a1', '144.bi1.a1', '360.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3256, -1, 2920, -1, 2698, -1, 5408, -1], 'generators': [3669134, 120, 50803200, 16], 'label': '2880.hl.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536492
    {'ambient': '2880.hl', 'aut_centralizer_order': 5, 'aut_label': '8.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '576.8311', 'aut_weyl_index': 5, 'centralizer': '576.a1.a1', 'complements': ['360.bz1.a1', '360.by1.a1', '360.cb1.a1', '360.ca1.a1', '360.ch1.a1', '360.cg1.a1', '360.cj1.a1', '360.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.br1.a1', '32.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1507, 7245, 1234, 6760, 780, 2507, 684, 7027], 'generators': [11, 124, 23, 1456, 50803200, 7], 'label': '2880.hl.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8311'}
  • id: 183536493
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.d1.a1', '36.i1.a1', '36.bi1.a1'], 'contains': ['144.c1.a1', '144.m1.a1', '144.n1.a1', '360.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1207, -1, 913, -1, 824, -1, 4115, -1], 'generators': [9, 120, 50803200, 16], 'label': '2880.hl.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '2880.hl', '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': '8.2'}
  • id: 183536494
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.d1.a1', '36.h1.a1', '36.bj1.a1'], 'contains': ['144.c1.a1', '144.o1.a1', '144.p1.a1', '360.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1554, -1, 1414, -1, 1738, -1, 3727, -1], 'generators': [3669138, 120, 50803200, 16], 'label': '2880.hl.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536495
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.b1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.bk1.a1'], 'contains': ['144.d1.a1', '144.e1.a1', '144.j1.a1', '144.u1.a1', '144.be1.a1', '360.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5649, -1, 5692, -1, 5612, -1, 8070, -1], 'generators': [5, 3669136, 50803200, 16], 'label': '2880.hl.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.h1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536496
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.j1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1', '36.bh1.a1'], 'contains': ['144.d1.a1', '144.f1.a1', '144.k1.a1', '144.v1.a1', '144.bh1.a1', '360.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6397, -1, 6643, -1, 5655, -1, 6917, -1], 'generators': [136, 3669120, 50803200, 7], 'label': '2880.hl.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536497
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.b1.a1', '36.o1.a1', '36.t1.a1', '36.u1.a1', '36.v1.a1', '36.w1.a1', '36.bl1.a1'], 'contains': ['144.d1.a1', '144.i1.a1', '144.l1.a1', '144.w1.a1', '144.bk1.a1', '360.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4678, -1, 4963, -1, 4718, -1, 8027, -1], 'generators': [23, 122, 3669143, 50803200], 'label': '2880.hl.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536498
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.a1.a1', '36.c1.a1', '36.k1.a1', '36.p1.a1', '36.t1.a1', '36.x1.a1', '36.y1.a1'], 'contains': ['144.b1.a1', '144.d1.a1', '144.x1.a1', '360.j1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8017, -1, 8021, -1, 7179, -1, 8224, -1], 'generators': [3669120, 8023687, 50803200, 7], 'label': '2880.hl.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536499
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '36.d1.a1', '36.o1.a1', '36.x1.a1', '36.z1.a1', '36.ba1.a1', '36.bb1.a1', '36.bk1.a1'], 'contains': ['144.d1.a1', '144.m1.a1', '144.o1.a1', '360.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1663, -1, 1213, -1, 3009, -1, 6517, -1], 'generators': [9, 3669136, 50803200, 16], 'label': '2880.hl.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536500
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.a1.a1', '36.e1.a1', '36.l1.a1', '36.q1.a1', '36.u1.a1', '36.z1.a1', '36.bc1.a1'], 'contains': ['144.d1.a1', '144.x1.a1', '360.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9434, -1, 9002, -1, 7613, -1, 7879, -1], 'generators': [3669120, 8023696, 50803200, 7], 'label': '2880.hl.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536501
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.c1.a1', '36.m1.a1', '36.q1.a1', '36.v1.a1', '36.ba1.a1', '36.bd1.a1', '36.bm1.a1'], 'contains': ['144.d1.a1', '144.y1.a1', '144.ba1.a1', '360.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8977, -1, 8846, -1, 7505, -1, 8145, -1], 'generators': [3669120, 8025247, 50803200, 7], 'label': '2880.hl.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536502
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '36.d1.a1', '36.j1.a1', '36.y1.a1', '36.bc1.a1', '36.bd1.a1', '36.be1.a1', '36.bl1.a1'], 'contains': ['144.d1.a1', '144.n1.a1', '144.p1.a1', '360.n1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1714, -1, 1883, -1, 2972, -1, 6480, -1], 'generators': [23, 130, 3669143, 50803200], 'label': '2880.hl.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536503
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 3, 'centralizer': '960.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '24.c1.a1', '24.bs1.a1', '32.b1.a1', '40.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4378, 4294, 3830, 4264, 4108, 5623, 1975, 4377], 'generators': [11, 23, 3669967, 1456, 50803200, 7], 'label': '2880.hl.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1', '4.h1.a1', '4.i1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '960.11361'}
  • id: 183536504
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '36.f1.a1', '36.l1.a1', '36.r1.a1', '36.w1.a1', '36.x1.a1', '36.bd1.a1', '36.bn1.a1'], 'contains': ['144.d1.a1', '144.bl1.a1', '360.o1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7066, -1, 6860, -1, 7035, -1, 8109, -1], 'generators': [8023697, 3669120, 50803200, 7], 'label': '2880.hl.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536505
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '36.g1.a1', '36.k1.a1', '36.s1.a1', '36.v1.a1', '36.z1.a1', '36.be1.a1', '36.bn1.a1'], 'contains': ['144.d1.a1', '144.z1.a1', '360.p1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9116, -1, 8747, -1, 7324, -1, 7801, -1], 'generators': [3669120, 8023686, 50803200, 7], 'label': '2880.hl.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536506
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '36.e1.a1', '36.n1.a1', '36.p1.a1', '36.w1.a1', '36.bb1.a1', '36.be1.a1', '36.bm1.a1'], 'contains': ['144.d1.a1', '144.ba1.a1', '360.q1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9187, -1, 9205, -1, 7781, -1, 7915, -1], 'generators': [8025256, 3669120, 50803200, 7], 'label': '2880.hl.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536507
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '36.g1.a1', '36.m1.a1', '36.r1.a1', '36.t1.a1', '36.bb1.a1', '36.bc1.a1', '36.bo1.a1'], 'contains': ['144.d1.a1', '144.bb1.a1', '360.r1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8801, -1, 8478, -1, 7143, -1, 7952, -1], 'generators': [23, 8025261, 3669143, 50803200], 'label': '2880.hl.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536508
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '36.f1.a1', '36.n1.a1', '36.s1.a1', '36.u1.a1', '36.y1.a1', '36.ba1.a1', '36.bo1.a1'], 'contains': ['144.d1.a1', '144.bm1.a1', '360.s1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7563, -1, 6823, -1, 6999, -1, 7988, -1], 'generators': [23, 8025253, 3669143, 50803200], 'label': '2880.hl.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536509
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '36.j1.a1', '36.bf1.a1', '36.bi1.a1'], 'contains': ['144.e1.a1', '144.f1.a1', '144.n1.a1', '360.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3388, -1, 3705, -1, 2827, -1, 3924, -1], 'generators': [127, 5, 50803200, 16], 'label': '2880.hl.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 183536510
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '36.b1.a1', '36.bf1.a1', '36.bp1.a1'], 'contains': ['144.e1.a1', '144.g1.a1', '144.l1.a1', '144.bd1.a1', '144.bf1.a1', '360.u1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3560, -1, 3959, -1, 3416, -1, 5173, -1], 'generators': [5, 3669856, 50803200, 16], 'label': '2880.hl.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536511
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '36.h1.a1', '36.bf1.a1', '36.bk1.a1'], 'contains': ['144.e1.a1', '144.h1.a1', '144.o1.a1', '360.v1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3721, -1, 3731, -1, 3285, -1, 3856, -1], 'generators': [5, 3669143, 50803200, 16], 'label': '2880.hl.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536512
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '36.h1.a1', '36.j1.a1', '36.bp1.a1'], 'contains': ['144.e1.a1', '144.k1.a1', '144.p1.a1', '360.w1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3469, -1, 3760, -1, 2918, -1, 3762, -1], 'generators': [5, 3669863, 50803200, 16], 'label': '2880.hl.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536513
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '36.bf1.a1', '36.bg1.a1', '36.bh1.a1'], 'contains': ['144.f1.a1', '144.g1.a1', '144.h1.a1', '144.bg1.a1', '144.bh1.a1', '360.x1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4563, -1, 4486, -1, 4132, -1, 5037, -1], 'generators': [136, 3669143, 50803200, 7], 'label': '2880.hl.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536514
    {'ambient': '2880.hl', 'aut_centralizer_order': 15, 'aut_label': '8.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 15, 'centralizer': '192.a1.a1', 'complements': ['360.cl1.a1', '360.cf1.a1', '360.bu1.a1', '360.bw1.a1', '360.bs1.a1', '360.cd1.a1', '360.cc1.a1', '360.bt1.a1', '360.ce1.a1', '360.ch1.a1', '360.cg1.a1', '360.cj1.a1', '360.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '24.d1.a1', '24.bt1.a1', '32.c1.a1', '40.b1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1190, 8734, 953, 8752, 1155, 1129, 492, 8871], 'generators': [11, 23, 1456, 5, 50803200, 7], 'label': '2880.hl.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1', '4.d1.a1', '4.j1.a1'], 'normal_contains': ['16.a1.a1', '24.d1.a1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1469'}
  • id: 183536515
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '36.o1.a1', '36.bg1.a1', '36.bi1.a1'], 'contains': ['144.f1.a1', '144.i1.a1', '144.m1.a1', '360.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2011, -1, 1484, -1, 2069, -1, 4692, -1], 'generators': [127, 9, 50803200, 16], 'label': '2880.hl.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 183536516
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '36.j1.a1', '36.bg1.a1', '36.bj1.a1'], 'contains': ['144.f1.a1', '144.j1.a1', '144.p1.a1', '360.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2977, -1, 1965, -1, 2616, -1, 4662, -1], 'generators': [3669134, 127, 50803200, 16], 'label': '2880.hl.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536517
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '36.o1.a1', '36.bf1.a1', '36.bj1.a1'], 'contains': ['144.f1.a1', '144.l1.a1', '144.o1.a1', '360.ba1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2109, -1, 2667, -1, 1862, -1, 3987, -1], 'generators': [3669138, 127, 50803200, 16], 'label': '2880.hl.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536518
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '36.b1.a1', '36.bg1.a1', '36.bq1.a1'], 'contains': ['144.g1.a1', '144.i1.a1', '144.j1.a1', '144.bj1.a1', '144.bn1.a1', '360.bb1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3306, -1, 2987, -1, 3085, -1, 5451, -1], 'generators': [3669134, 3669856, 50803200, 16], 'label': '2880.hl.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536519
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '36.d1.a1', '36.bg1.a1', '36.bp1.a1'], 'contains': ['144.g1.a1', '144.m1.a1', '144.p1.a1', '360.bc1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1404, -1, 1126, -1, 1494, -1, 4631, -1], 'generators': [9, 3669856, 50803200, 16], 'label': '2880.hl.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536520
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '36.d1.a1', '36.bf1.a1', '36.bq1.a1'], 'contains': ['144.g1.a1', '144.n1.a1', '144.o1.a1', '360.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1490, -1, 1183, -1, 1531, -1, 3887, -1], 'generators': [3669138, 3669856, 50803200, 16], 'label': '2880.hl.72.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536521
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '36.h1.a1', '36.bg1.a1', '36.bl1.a1'], 'contains': ['144.h1.a1', '144.i1.a1', '144.p1.a1', '360.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2162, -1, 2010, -1, 2257, -1, 4012, -1], 'generators': [23, 122, 3669136, 50803200], 'label': '2880.hl.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536522
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '36.i1.a1', '36.bg1.a1', '36.bk1.a1'], 'contains': ['144.h1.a1', '144.j1.a1', '144.m1.a1', '360.bf1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2852, -1, 1159, -1, 2592, -1, 4576, -1], 'generators': [9, 3669143, 50803200, 16], 'label': '2880.hl.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536523
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '36.i1.a1', '36.bf1.a1', '36.bl1.a1'], 'contains': ['144.h1.a1', '144.l1.a1', '144.n1.a1', '360.bg1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1813, -1, 2686, -1, 1796, -1, 4081, -1], 'generators': [23, 130, 3669136, 50803200], 'label': '2880.hl.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536524
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1.a1', '36.h1.a1', '36.o1.a1', '36.bq1.a1'], 'contains': ['144.i1.a1', '144.k1.a1', '144.o1.a1', '360.bh1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2181, -1, 1858, -1, 2282, -1, 3832, -1], 'generators': [3669138, 3669863, 50803200, 16], 'label': '2880.hl.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536525
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 3, 'centralizer': '960.a1.a1', 'complements': ['1440.b1.a1', '1440.e1.a1', '1440.f1.a1', '1440.j1.a1', '1440.h1.a1', '1440.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.f1.a1', '4.h1.a1', '6.b1.a1', '6.p1.a1', '8.k1.a1', '10.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5542, 1601, 5702, 1755, 5569, 7542, 2088, 2458], 'generators': [11, 23, 3669967, 1456, 5, 8025137, 50803200, 7], 'label': '2880.hl.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.f1.a1', '4.h1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '2880.hl', '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': '960.11361'}
  • id: 183536526
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '8.d1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['360.bz1.a1', '360.by1.a1', '360.cb1.a1', '360.ca1.a1', '360.ch1.a1', '360.cg1.a1', '360.cj1.a1', '360.ci1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.e1.a1', '24.bu1.a1', '32.d1.a1', '40.e1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1608, 5249, 1582, 5267, 910, 4355, 377, 5645], 'generators': [11, 23, 1456, 3669848, 50803200, 7], 'label': '2880.hl.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'normal_contains': ['16.a1.a1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536527
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1.a1', '36.i1.a1', '36.j1.a1', '36.bq1.a1'], 'contains': ['144.j1.a1', '144.k1.a1', '144.n1.a1', '360.bi1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2503, -1, 1839, -1, 2640, -1, 4148, -1], 'generators': [3669134, 3669863, 50803200, 16], 'label': '2880.hl.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536528
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1.a1', '36.i1.a1', '36.o1.a1', '36.bp1.a1'], 'contains': ['144.k1.a1', '144.l1.a1', '144.m1.a1', '360.bj1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1627, -1, 2556, -1, 1772, -1, 4509, -1], 'generators': [9, 3669863, 50803200, 16], 'label': '2880.hl.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536529
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.br1.a1', '36.bh1.a1', '36.bi1.a1', '36.bj1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.f1.a1', '360.bk1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2590, -1, 1281, -1, 907, -1, 2847, -1], 'generators': [127, 23, 50803200, 7], 'label': '2880.hl.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536530
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.bt1.a1', '36.bi1.a1', '36.bk1.a1', '36.bp1.a1'], 'contains': ['144.a1.a1', '144.e1.a1', '144.m1.a1', '360.bm1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1084, -1, 740, -1, 650, -1, 2779, -1], 'generators': [23, 5, 50803200, 7], 'label': '2880.hl.72.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 183536531
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.bu1.a1', '36.bh1.a1', '36.bp1.a1', '36.bq1.a1'], 'contains': ['144.a1.a1', '144.g1.a1', '144.k1.a1', '360.bn1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1761, -1, 2522, -1, 1455, -1, 2740, -1], 'generators': [23, 3669863, 50803200, 7], 'label': '2880.hl.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536532
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.10', 'aut_weyl_index': 180, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '24.bw1.a1', '24.bx1.a1', '36.bi1.a1', '36.bl1.a1', '36.bq1.a1'], 'contains': ['144.a1.a1', '144.i1.a1', '144.n1.a1', '360.bo1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1123, -1, 769, -1, 588, -1, 2700, -1], 'generators': [23, 122, 50803200, 7], 'label': '2880.hl.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 183536533
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.by1.a1', '36.bj1.a1', '36.bk1.a1', '36.bq1.a1'], 'contains': ['144.a1.a1', '144.j1.a1', '144.o1.a1', '360.bp1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1235, -1, 857, -1, 680, -1, 2810, -1], 'generators': [3669138, 23, 50803200, 7], 'label': '2880.hl.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536534
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '24.ca1.a1', '24.cb1.a1', '36.bj1.a1', '36.bl1.a1', '36.bp1.a1'], 'contains': ['144.a1.a1', '144.l1.a1', '144.p1.a1', '360.bq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1147, -1, 884, -1, 619, -1, 2669, -1], 'generators': [23, 3669850, 50803200, 7], 'label': '2880.hl.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536535
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.a1', '24.cf1.a1', '36.b1.a1', '36.br1.a1', '36.bs1.a1'], 'contains': ['144.q1.a1', '144.r1.a1', '144.t1.a1', '144.u1.a1', '144.w1.a1', '144.bd1.a1', '144.bj1.a1', '360.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4437, -1, 4399, -1, 4676, -1, 9061, -1], 'generators': [5, 3669120, 120, 50803200], 'label': '2880.hl.72.br1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536536
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.cd1.a1', '36.c1.a1', '36.br1.a1'], 'contains': ['144.b1.a1', '144.q1.a1', '144.y1.a1', '360.bs1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7910, -1, 7893, -1, 6770, -1, 6278, -1], 'generators': [3669120, 8023680, 120, 50803200], 'label': '2880.hl.72.bs1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536537
    {'ambient': '2880.hl', 'aut_centralizer_order': 5, 'aut_label': '8.e1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '576.8311', 'aut_weyl_index': 5, 'centralizer': '576.a1.a1', 'complements': ['360.cl1.a1', '360.cf1.a1', '360.bu1.a1', '360.bw1.a1', '360.bs1.a1', '360.cd1.a1', '360.cc1.a1', '360.bt1.a1', '360.ce1.a1', '360.ca1.a1', '360.cb1.a1', '360.bz1.a1', '360.by1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.e1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.bv1.a1', '24.bw1.a1', '24.bx1.a1', '32.e1.a1', '40.c1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1305, 8041, 1186, 8059, 998, 1771, 634, 8229], 'generators': [11, 23, 122, 1456, 50803200, 7], 'label': '2880.hl.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.b1.a1', '4.e1.a1', '4.k1.a1'], 'normal_contains': ['16.a1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8311'}
  • id: 183536538
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '36.c1.a1', '36.e1.a1', '36.bs1.a1'], 'contains': ['144.q1.a1', '144.x1.a1', '144.ba1.a1', '360.bt1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9566, -1, 9263, -1, 7685, -1, 8804, -1], 'generators': [3669120, 8023687, 120, 50803200], 'label': '2880.hl.72.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536539
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ce1.a1', '24.ch1.a1', '36.g1.a1', '36.br1.a1', '36.bs1.a1'], 'contains': ['144.q1.a1', '144.z1.a1', '144.bb1.a1', '360.bu1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9029, -1, 8653, -1, 6914, -1, 8297, -1], 'generators': [3669120, 8023686, 120, 50803200], 'label': '2880.hl.72.bu1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536540
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '36.b1.a1'], 'contains': ['144.r1.a1', '144.s1.a1', '144.t1.a1', '144.be1.a1', '144.bf1.a1', '144.bk1.a1', '144.bn1.a1', '360.bv1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5092, -1, 5145, -1, 5106, -1, 9981, -1], 'generators': [5, 3669136, 120, 50803200], 'label': '2880.hl.72.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536541
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1.a1', '36.f1.a1'], 'contains': ['144.s1.a1', '144.bl1.a1', '144.bm1.a1', '360.bw1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6621, -1, 6562, -1, 6661, -1, 9643, -1], 'generators': [8023697, 3669127, 120, 50803200], 'label': '2880.hl.72.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536542
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '36.b1.a1', '36.bt1.a1', '36.bu1.a1'], 'contains': ['144.u1.a1', '144.v1.a1', '144.w1.a1', '144.bc1.a1', '144.bf1.a1', '144.bi1.a1', '144.bn1.a1', '360.bx1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5420, -1, 5428, -1, 5252, -1, 9762, -1], 'generators': [136, 5, 3669120, 50803200], 'label': '2880.hl.72.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536543
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '24.cp1.a1', '36.k1.a1', '36.br1.a1', '36.bt1.a1'], 'contains': ['144.b1.a1', '144.u1.a1', '144.z1.a1', '360.by1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7964, -1, 8422, -1, 6842, -1, 8369, -1], 'generators': [5, 8023685, 3669120, 50803200], 'label': '2880.hl.72.by1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '72.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536544
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1.a1', '36.k1.a1', '36.bs1.a1', '36.bu1.a1'], 'contains': ['144.u1.a1', '144.x1.a1', '144.z1.a1', '360.bz1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9492, -1, 9048, -1, 7432, -1, 8913, -1], 'generators': [8023694, 5, 3669120, 50803200], 'label': '2880.hl.72.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '72.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536545
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '24.cq1.a1', '36.m1.a1', '36.br1.a1', '36.bu1.a1'], 'contains': ['144.u1.a1', '144.y1.a1', '144.bb1.a1', '360.ca1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8741, -1, 8351, -1, 6878, -1, 8405, -1], 'generators': [5, 8025245, 3669120, 50803200], 'label': '2880.hl.72.ca1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536546
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.a1', '36.m1.a1', '36.bs1.a1', '36.bt1.a1'], 'contains': ['144.u1.a1', '144.ba1.a1', '144.bb1.a1', '360.cb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9330, -1, 9077, -1, 7360, -1, 8840, -1], 'generators': [5, 8025254, 3669120, 50803200], 'label': '2880.hl.72.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536547
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '36.c1.a1', '36.p1.a1', '36.bt1.a1'], 'contains': ['144.b1.a1', '144.v1.a1', '144.ba1.a1', '360.cc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8470, -1, 8580, -1, 7468, -1, 8526, -1], 'generators': [127, 3669120, 8023680, 50803200], 'label': '2880.hl.72.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536548
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '8.f1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '960.11361', 'aut_weyl_index': 3, 'centralizer': '960.a1.a1', 'complements': ['360.cl1.a1', '360.cf1.a1', '360.bu1.a1', '360.bw1.a1', '360.bs1.a1', '360.cc1.a1', '360.cd1.a1', '360.bt1.a1', '360.ce1.a1', '360.cg1.a1', '360.ch1.a1', '360.ci1.a1', '360.cj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.f1.a1', '24.by1.a1', '32.f1.a1', '40.f1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1458, 5947, 1039, 5964, 1079, 3709, 579, 6291], 'generators': [11, 23, 1456, 3669969, 50803200, 7], 'label': '2880.hl.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.c1.a1', '4.d1.a1', '4.k1.a1'], 'normal_contains': ['16.a1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '960.11361'}
  • id: 183536549
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '36.c1.a1', '36.q1.a1', '36.bu1.a1'], 'contains': ['144.v1.a1', '144.x1.a1', '144.y1.a1', '360.cd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9360, -1, 8802, -1, 7577, -1, 8671, -1], 'generators': [127, 3669120, 8023687, 50803200], 'label': '2880.hl.72.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536550
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.a1', '36.e1.a1', '36.p1.a1', '36.q1.a1'], 'contains': ['144.v1.a1', '144.x1.a1', '144.ba1.a1', '360.ce1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9529, -1, 9235, -1, 7745, -1, 8598, -1], 'generators': [127, 3669120, 8023696, 50803200], 'label': '2880.hl.72.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.ce1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536551
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.g1.a1', '36.bt1.a1', '36.bu1.a1'], 'contains': ['144.v1.a1', '144.z1.a1', '144.bb1.a1', '360.cf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9063, -1, 8624, -1, 7216, -1, 8562, -1], 'generators': [127, 3669120, 8023686, 50803200], 'label': '2880.hl.72.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536552
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '24.cz1.a1', '24.db1.a1', '36.t1.a1', '36.br1.a1', '36.bt1.a1'], 'contains': ['144.b1.a1', '144.w1.a1', '144.bb1.a1', '360.cg1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8055, -1, 7946, -1, 6734, -1, 8261, -1], 'generators': [3669120, 8025261, 8023680, 50803200], 'label': '2880.hl.72.cg1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536553
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1.a1', '36.t1.a1', '36.bs1.a1', '36.bu1.a1'], 'contains': ['144.w1.a1', '144.x1.a1', '144.bb1.a1', '360.ch1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9462, -1, 8880, -1, 7396, -1, 8877, -1], 'generators': [8023703, 3669120, 8025261, 50803200], 'label': '2880.hl.72.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ch1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536554
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1.a1', '24.da1.a1', '36.v1.a1', '36.br1.a1', '36.bu1.a1'], 'contains': ['144.w1.a1', '144.y1.a1', '144.z1.a1', '360.ci1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8921, -1, 8540, -1, 7071, -1, 8333, -1], 'generators': [8023682, 122, 3669120, 50803200], 'label': '2880.hl.72.ci1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ci1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536555
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1.a1', '36.v1.a1', '36.bs1.a1', '36.bt1.a1'], 'contains': ['144.w1.a1', '144.z1.a1', '144.ba1.a1', '360.cj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9388, -1, 9112, -1, 7541, -1, 8768, -1], 'generators': [122, 3669120, 8023701, 50803200], 'label': '2880.hl.72.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536556
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1.a1', '36.b1.a1'], 'contains': ['144.bc1.a1', '144.bd1.a1', '144.be1.a1', '144.bg1.a1', '144.bi1.a1', '144.bj1.a1', '144.bk1.a1', '360.ck1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5126, -1, 5278, -1, 5064, -1, 9865, -1], 'generators': [136, 5, 3669136, 50803200], 'label': '2880.hl.72.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ck1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536557
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1.a1', '36.f1.a1'], 'contains': ['144.bg1.a1', '144.bl1.a1', '144.bm1.a1', '360.cl1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6592, -1, 6532, -1, 6625, -1, 9405, -1], 'generators': [127, 8023697, 3669127, 50803200], 'label': '2880.hl.72.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.cl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536558
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '80.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '48.d1.a1', 'complements': ['36.bu1.a1', '36.bt1.a1', '36.br1.a1', '36.bs1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1', '40.d1.a1', '40.e1.a1', '40.f1.a1', '40.g1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.q1.a1', '320.a1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [12, 7245, 12, 7424, 88, 2903, 274, 7082], 'generators': [11, 23, 1456, 7], 'label': '2880.hl.80.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1'], 'normal_contains': ['240.a1.a1', '240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.5', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536559
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '8.g1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['360.cl1.a1', '360.bu1.a1', '360.cf1.a1', '360.bw1.a1', '360.bs1.a1', '360.cd1.a1', '360.cc1.a1', '360.bt1.a1', '360.ce1.a1', '360.ca1.a1', '360.cb1.a1', '360.bz1.a1', '360.by1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.e1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '24.bz1.a1', '24.ca1.a1', '24.cb1.a1', '32.g1.a1', '40.g1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1388, 6552, 1154, 7453, 1117, 3149, 541, 7669], 'generators': [11, 23, 1456, 3669850, 50803200, 7], 'label': '2880.hl.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.a1', '4.e1.a1', '4.j1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536560
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '20.b1.a1', '40.h1.a1', '40.i1.a1', '40.j1.a1'], 'contains': ['160.a1.a1', '160.b1.a1', '160.d1.a1', '240.r1.a1', '240.u1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [626, -1, 825, -1, 711, -1, 1307, -1], 'generators': [124, 1440, 3669960, 3], 'label': '2880.hl.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536561
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '20.a1.a1', '40.h1.a1'], 'contains': ['160.a1.a1', '160.c1.a1', '160.e1.a1', '240.s1.a1', '240.v1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1940, -1, 2306, -1, 1252, -1, 345, -1], 'generators': [124, 1440, 5, 3], 'label': '2880.hl.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '80.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536562
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '20.c1.a1', '40.h1.a1'], 'contains': ['160.a1.a1', '160.f1.a1', '160.g1.a1', '240.t1.a1', '240.x1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [869, -1, 561, -1, 559, -1, 323, -1], 'generators': [1440, 128, 3669974, 12], 'label': '2880.hl.80.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536563
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '20.d1.a1', '40.h1.a1', '40.k1.a1', '40.l1.a1'], 'contains': ['160.b1.a1', '160.c1.a1', '160.f1.a1', '240.y1.a1', '240.z1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3131, -1, 3534, -1, 2562, -1, 559, -1], 'generators': [11, 1440, 3669960, 5], 'label': '2880.hl.80.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536564
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '20.e1.a1', '40.h1.a1', '40.m1.a1', '40.n1.a1'], 'contains': ['160.b1.a1', '160.e1.a1', '160.g1.a1', '240.bb1.a1', '240.bc1.a1', '240.bd1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2660, -1, 3280, -1, 3129, -1, 1220, -1], 'generators': [1440, 3669960, 122, 12], 'label': '2880.hl.80.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536565
    {'ambient': '2880.hl', 'aut_centralizer_order': 36, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '80.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '20.f1.a1', '40.i1.a1', '40.k1.a1', '40.m1.a1'], 'contains': ['160.b1.a1', '240.be1.a1', '240.bk1.a1', '240.bo1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5828, -1, 5995, -1, 6257, -1, 1854, -1], 'generators': [1440, 8025132, 3669960, 12], 'label': '2880.hl.80.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536566
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '20.g1.a1', '40.i1.a1', '40.l1.a1', '40.n1.a1'], 'contains': ['160.b1.a1', '240.bg1.a1', '240.bl1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5928, -1, 6096, -1, 5895, -1, 1641, -1], 'generators': [1440, 3669960, 8025255, 20], 'label': '2880.hl.80.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536567
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '20.h1.a1', '40.j1.a1', '40.k1.a1', '40.n1.a1'], 'contains': ['160.b1.a1', '240.bh1.a1', '240.bm1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6461, -1, 6421, -1, 6128, -1, 1514, -1], 'generators': [11, 1440, 3669960, 8025126], 'label': '2880.hl.80.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536568
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '80.j1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '20.i1.a1', '40.j1.a1', '40.l1.a1', '40.m1.a1'], 'contains': ['160.b1.a1', '240.bj1.a1', '240.bn1.a1', '240.bp1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6325, -1, 6358, -1, 6293, -1, 1796, -1], 'generators': [11, 1440, 3669960, 8025261], 'label': '2880.hl.80.j1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536569
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '80.k1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '20.j1.a1', '40.h1.a1'], 'contains': ['160.c1.a1', '160.d1.a1', '160.g1.a1', '240.br1.a1', '240.bu1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1492, -1, 2264, -1, 1100, -1, 148, -1], 'generators': [1440, 5, 3669844, 3], 'label': '2880.hl.80.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536570
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.k1.a1', '16.l1.a1', '24.cc1.a1', '24.cf1.a1', '40.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3087, -1, 2818, -1, 1483, -1, 1095, -1], 'generators': [124, 1440, 3669960, 5, 3, 50803200], 'label': '2880.hl.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.h1.a1', 'projective_image': '2880.hl', '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': '720.783'}
  • id: 183536571
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '80.l1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '20.k1.a1', '40.h1.a1'], 'contains': ['160.d1.a1', '160.e1.a1', '160.f1.a1', '240.by1.a1', '240.bz1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [954, -1, 518, -1, 1011, -1, 190, -1], 'generators': [1440, 3669974, 12, 3669848], 'label': '2880.hl.80.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '80.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536572
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.a1.a1', '45.a1.a1'], 'contains': ['180.a1.a1', '180.b1.a1', '180.f1.a1', '180.j1.a1', '180.l1.a1', '180.s1.a1', '180.u1.a1', '180.br1.a1', '180.bs1.a1', '180.bt1.a1', '180.bu1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8687, -1, 9199, -1, 9714, -1, 6311, -1], 'generators': [8023694, 5, 3669136, 120, 16], 'label': '2880.hl.90.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536573
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.b1.a1', '45.a1.a1'], 'contains': ['180.a1.a1', '180.d1.a1', '180.e1.a1', '180.k1.a1', '180.m1.a1', '180.t1.a1', '180.v1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7166, -1, 7373, -1, 8496, -1, 6937, -1], 'generators': [5, 8023698, 3669136, 120, 16], 'label': '2880.hl.90.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536574
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.c1.a1', '45.a1.a1'], 'contains': ['180.b1.a1', '180.c1.a1', '180.e1.a1', '180.w1.a1', '180.x1.a1', '180.z1.a1', '180.bc1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7474, -1, 7592, -1, 8363, -1, 5910, -1], 'generators': [8023698, 9, 3669136, 120, 16], 'label': '2880.hl.90.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536575
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '30.d1.a1', '45.a1.a1'], 'contains': ['180.c1.a1', '180.d1.a1', '180.f1.a1', '180.y1.a1', '180.ba1.a1', '180.bb1.a1', '180.bd1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9834, -1, 9927, -1, 9227, -1, 5723, -1], 'generators': [8023694, 9, 3669136, 120, 16], 'label': '2880.hl.90.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536576
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '30.e1.a1', '45.a1.a1'], 'contains': ['180.i1.a1', '180.j1.a1', '180.m1.a1', '180.o1.a1', '180.r1.a1', '180.x1.a1', '180.bd1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7735, -1, 7731, -1, 8681, -1, 5871, -1], 'generators': [127, 8023694, 5, 3669136, 16], 'label': '2880.hl.90.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536577
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.f1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '30.f1.a1', '45.a1.a1'], 'contains': ['180.i1.a1', '180.k1.a1', '180.l1.a1', '180.p1.a1', '180.q1.a1', '180.bb1.a1', '180.bc1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7538, -1, 8141, -1, 8911, -1, 6044, -1], 'generators': [127, 5, 8023698, 3669136, 16], 'label': '2880.hl.90.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536578
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.g1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '30.g1.a1', '45.a1.a1'], 'contains': ['180.n1.a1', '180.o1.a1', '180.q1.a1', '180.s1.a1', '180.v1.a1', '180.w1.a1', '180.ba1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7576, -1, 8027, -1, 8838, -1, 6171, -1], 'generators': [127, 8023698, 9, 3669136, 16], 'label': '2880.hl.90.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536579
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.h1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '30.h1.a1', '45.a1.a1'], 'contains': ['180.n1.a1', '180.p1.a1', '180.r1.a1', '180.t1.a1', '180.u1.a1', '180.y1.a1', '180.z1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8048, -1, 7682, -1, 8565, -1, 5764, -1], 'generators': [127, 8023694, 9, 3669136, 16], 'label': '2880.hl.90.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536580
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.i1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '30.i1.a1', '30.l1.a1', '45.a1.a1'], 'contains': ['180.a1.a1', '180.c1.a1', '180.g1.a1', '180.h1.a1', '180.i1.a1', '180.n1.a1', '180.be1.a1', '180.bf1.a1', '180.bg1.a1', '180.bh1.a1', '180.bi1.a1', '180.bj1.a1', '180.bk1.a1', '180.bp1.a1', '180.bq1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1883, -1, 2075, -1, 2434, -1, 3302, -1], 'generators': [127, 23, 5, 3669143, 7], 'label': '2880.hl.90.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536581
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.g1.a1', '16.h1.a1', '24.g1.a1', '24.cd1.a1', '40.i1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5344, -1, 5391, -1, 5175, -1, 2608, -1], 'generators': [1440, 8025132, 3669960, 128, 12, 50803200], 'label': '2880.hl.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536582
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '90.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '30.j1.a1', '30.m1.a1', '45.a1.a1'], 'contains': ['180.b1.a1', '180.d1.a1', '180.o1.a1', '180.p1.a1', '180.bg1.a1', '180.bl1.a1', '180.bm1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8542, -1, 8785, -1, 9813, -1, 5146, -1], 'generators': [127, 23, 3669143, 8023696, 7], 'label': '2880.hl.90.j1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536583
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.k1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '30.k1.a1', '30.n1.a1', '45.a1.a1'], 'contains': ['180.e1.a1', '180.f1.a1', '180.q1.a1', '180.r1.a1', '180.bg1.a1', '180.bn1.a1', '180.bo1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7293, -1, 7451, -1, 8117, -1, 5018, -1], 'generators': [127, 23, 8023697, 3669143, 7], 'label': '2880.hl.90.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536584
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '90.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.a1', '30.o1.a1', '30.q1.a1', '45.a1.a1'], 'contains': ['180.j1.a1', '180.k1.a1', '180.w1.a1', '180.y1.a1', '180.bj1.a1', '180.bl1.a1', '180.bn1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7394, -1, 7968, -1, 8645, -1, 4449, -1], 'generators': [23, 8023694, 5, 3669143, 7], 'label': '2880.hl.90.l1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '90.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536585
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.m1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '30.p1.a1', '30.r1.a1', '45.a1.a1'], 'contains': ['180.l1.a1', '180.m1.a1', '180.z1.a1', '180.ba1.a1', '180.bj1.a1', '180.bm1.a1', '180.bo1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7986, -1, 7416, -1, 8402, -1, 4924, -1], 'generators': [23, 5, 8025254, 3669143, 7], 'label': '2880.hl.90.m1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536586
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.n1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '30.s1.a1', '30.u1.a1', '30.w1.a1', '45.a1.a1'], 'contains': ['180.s1.a1', '180.t1.a1', '180.x1.a1', '180.bb1.a1', '180.bk1.a1', '180.bl1.a1', '180.bo1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7631, -1, 7511, -1, 8160, -1, 4486, -1], 'generators': [23, 8025253, 3669143, 8023696, 7], 'label': '2880.hl.90.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536587
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '90.o1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1.a1', '30.t1.a1', '30.v1.a1', '45.a1.a1'], 'contains': ['180.u1.a1', '180.v1.a1', '180.bc1.a1', '180.bd1.a1', '180.bk1.a1', '180.bm1.a1', '180.bn1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7251, -1, 8086, -1, 8875, -1, 4412, -1], 'generators': [23, 122, 8023693, 3669143, 7], 'label': '2880.hl.90.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536588
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '96.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '24.d1.a1', 'complements': ['30.q1.a1', '30.r1.a1', '30.u1.a1', '30.w1.a1', '30.v1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.c1.a1', '48.f1.a1', '48.x1.a1', '48.y1.a1', '48.z1.a1'], 'contains': ['192.a1.a1', '288.c1.a1', '480.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4058, 4015, 4123, 3993, 4329, 5024, 8273, 4960], 'generators': [1440, 120, 50803200], 'label': '2880.hl.96.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1', '480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536589
    {'ambient': '2880.hl', 'aut_centralizer_order': 72, 'aut_label': '96.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '40.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.g1.a1', '48.ba1.a1', '48.bc1.a1', '48.bd1.a1', '48.bg1.a1', '48.bh1.a1', '48.bi1.a1', '48.bj1.a1'], 'contains': ['192.a1.a1', '288.a1.a1', '480.d1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6783, 2243, 6917, 2378, 6432, 7025, 8438, 3140], 'generators': [1440, 3669960, 50803200], 'label': '2880.hl.96.b1.a1', 'mobius_quo': 0, 'mobius_sub': -96, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['24.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1'], 'normal_contains': ['192.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '2880.hl', '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': '40.12'}
  • id: 183536590
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '96.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '120.b1.a1', 'complements': ['30.q1.a1', '30.r1.a1', '30.u1.a1', '30.w1.a1', '30.v1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.c1.a1', '48.j1.a1', '48.br1.a1', '48.bv1.a1', '48.bz1.a1'], 'contains': ['192.a1.a1', '288.f1.a1', '480.k1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4026, 3541, 4242, 3519, 4378, 5463, 8243, 4522], 'generators': [1440, 3669840, 50803200], 'label': '2880.hl.96.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['24.e1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536591
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '24.bt1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1', '48.m1.a1', '48.n1.a1', '48.o1.a1', '48.p1.a1', '48.q1.a1', '48.r1.a1', '48.s1.a1'], 'contains': ['192.a1.a1', '288.b1.a1', '480.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3783, -1, 3614, -1, 3519, -1, 4694, -1], 'generators': [1447, 50803200, 7], 'label': '2880.hl.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536592
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.j1.a1', '24.ce1.a1', '24.ch1.a1', '40.j1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6247, -1, 6344, -1, 5558, -1, 2558, -1], 'generators': [124, 1440, 3669960, 8025121, 3, 50803200], 'label': '2880.hl.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536593
    {'ambient': '2880.hl', 'aut_centralizer_order': 30, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '32.a1.a1', '48.u1.a1', '48.v1.a1', '48.w1.a1'], 'contains': ['192.b1.a1', '288.c1.a1', '480.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2606, -1, 1489, -1, 750, -1, 1025, -1], 'generators': [124, 3, 50803200], 'label': '2880.hl.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '96.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536594
    {'ambient': '2880.hl', 'aut_centralizer_order': 18, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '32.b1.a1', '48.u1.a1', '48.bb1.a1', '48.be1.a1', '48.bk1.a1', '48.bl1.a1', '48.bm1.a1', '48.bn1.a1'], 'contains': ['192.b1.a1', '288.a1.a1', '480.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4087, -1, 4156, -1, 4646, -1, 2044, -1], 'generators': [11, 3669120, 50803200], 'label': '2880.hl.96.f1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '96.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536595
    {'ambient': '2880.hl', 'aut_centralizer_order': 9, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '32.b1.a1', '48.bf1.a1', '48.bo1.a1', '48.bp1.a1'], 'contains': ['192.c1.a1', '288.a1.a1', '480.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4247, -1, 4349, -1, 4914, -1, 1998, -1], 'generators': [1443, 3669964, 50803200], 'label': '2880.hl.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '96.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536596
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.h1.a1', '48.x1.a1', '48.ba1.a1', '48.bq1.a1', '48.br1.a1', '48.bs1.a1', '48.bt1.a1'], 'contains': ['192.a1.a1', '288.d1.a1', '480.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5309, -1, 5087, -1, 4784, -1, 8760, -1], 'generators': [1440, 5, 50803200], 'label': '2880.hl.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536597
    {'ambient': '2880.hl', 'aut_centralizer_order': 30, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '32.c1.a1', '48.v1.a1', '48.bb1.a1', '48.bu1.a1'], 'contains': ['192.b1.a1', '288.d1.a1', '480.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2845, -1, 2980, -1, 1439, -1, 835, -1], 'generators': [11, 5, 50803200], 'label': '2880.hl.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '96.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536598
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '72.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.i1.a1', '48.bc1.a1', '48.bq1.a1', '48.bv1.a1', '48.bw1.a1', '48.bx1.a1'], 'contains': ['192.a1.a1', '288.e1.a1', '480.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5714, -1, 5652, -1, 5144, -1, 8522, -1], 'generators': [127, 1440, 50803200], 'label': '2880.hl.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536599
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '32.d1.a1', '48.u1.a1', '48.bu1.a1', '48.by1.a1'], 'contains': ['192.b1.a1', '288.f1.a1', '480.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2583, -1, 1625, -1, 781, -1, 755, -1], 'generators': [12, 3669848, 50803200], 'label': '2880.hl.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '96.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536600
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.k1.a1', '48.y1.a1', '48.bs1.a1', '48.bv1.a1', '48.bw1.a1', '48.ca1.a1', '48.cb1.a1', '48.cc1.a1'], 'contains': ['192.a1.a1', '288.g1.a1', '480.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5914, -1, 5842, -1, 5731, -1, 8607, -1], 'generators': [1440, 3669967, 50803200], 'label': '2880.hl.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536601
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.l1.a1', '48.x1.a1', '48.bd1.a1', '48.bq1.a1', '48.bz1.a1', '48.ca1.a1', '48.cd1.a1'], 'contains': ['192.a1.a1', '288.h1.a1', '480.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4354, -1, 4494, -1, 4490, -1, 8730, -1], 'generators': [1440, 122, 50803200], 'label': '2880.hl.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536602
    {'ambient': '2880.hl', 'aut_centralizer_order': 10, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '32.e1.a1', '48.v1.a1', '48.be1.a1', '48.by1.a1'], 'contains': ['192.b1.a1', '288.h1.a1', '480.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2485, -1, 1682, -1, 1323, -1, 995, -1], 'generators': [122, 12, 50803200], 'label': '2880.hl.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '96.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536603
    {'ambient': '2880.hl', 'aut_centralizer_order': 3, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '4.l1.a1'], 'contains': ['16.e1.a1', '16.g1.a1', '16.i1.a1', '24.cl1.a1', '24.cp1.a1', '40.k1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5550, -1, 5692, -1, 5619, -1, 2109, -1], 'generators': [11, 1440, 3669960, 5, 8025126, 50803200], 'label': '2880.hl.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536604
    {'ambient': '2880.hl', 'aut_centralizer_order': 5, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a1', '32.e1.a1', '48.bf1.a1'], 'contains': ['192.c1.a1', '288.h1.a1', '480.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2772, -1, 2305, -1, 1403, -1, 1198, -1], 'generators': [122, 1443, 50803200], 'label': '2880.hl.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.db1.a1', 'old_label': '96.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536605
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.m1.a1', '48.z1.a1', '48.ba1.a1', '48.bs1.a1', '48.bx1.a1', '48.bz1.a1', '48.cd1.a1'], 'contains': ['192.a1.a1', '288.i1.a1', '480.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5171, -1, 4768, -1, 4526, -1, 8790, -1], 'generators': [1440, 3669974, 50803200], 'label': '2880.hl.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536606
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '32.f1.a1', '48.w1.a1', '48.bb1.a1', '48.by1.a1'], 'contains': ['192.b1.a1', '288.i1.a1', '480.q1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2542, -1, 1584, -1, 1257, -1, 925, -1], 'generators': [11, 3669125, 50803200], 'label': '2880.hl.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '96.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536607
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.n1.a1', '48.y1.a1', '48.bc1.a1', '48.bt1.a1', '48.bw1.a1', '48.cd1.a1'], 'contains': ['192.a1.a1', '288.j1.a1', '480.r1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5494, -1, 5497, -1, 5174, -1, 8552, -1], 'generators': [1440, 3669863, 50803200], 'label': '2880.hl.96.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536608
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '48.o1.a1', '48.z1.a1', '48.bd1.a1', '48.br1.a1', '48.bt1.a1', '48.bx1.a1', '48.ca1.a1'], 'contains': ['192.a1.a1', '288.k1.a1', '480.s1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4796, -1, 4887, -1, 4460, -1, 8700, -1], 'generators': [1440, 3669842, 50803200], 'label': '2880.hl.96.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '96.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536609
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '32.g1.a1', '48.w1.a1', '48.be1.a1', '48.bu1.a1'], 'contains': ['192.b1.a1', '288.k1.a1', '480.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2698, -1, 1650, -1, 969, -1, 805, -1], 'generators': [3669842, 12, 50803200], 'label': '2880.hl.96.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '96.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536610
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1.a1', '32.g1.a1', '48.bf1.a1'], 'contains': ['192.c1.a1', '288.k1.a1', '480.u1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2812, -1, 2362, -1, 1195, -1, 1158, -1], 'generators': [1443, 3669842, 50803200], 'label': '2880.hl.96.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.db1.a1', 'old_label': '96.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 183536611
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '120.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '36.a1.a1', 'complements': ['24.cp1.a1', '24.cq1.a1', '24.cz1.a1', '24.db1.a1', '24.da1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.bj1.a1', '60.bk1.a1', '60.bl1.a1'], 'contains': ['240.a1.a1', '240.c1.a1', '240.f1.a1', '360.bk1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2780, 5964, 2035, 5753, 2750, 3474, 2518, 6510], 'generators': [127, 23, 1456, 7], 'label': '2880.hl.120.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1'], 'normal_contains': ['240.a1.a1', '480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '6.1', 'quotient_action_kernel': '20.3', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536612
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '120.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '24.g1.a1', 'complements': ['24.dd1.a1', '24.cu1.a1', '24.ch1.a1', '24.cj1.a1', '24.g1.a1', '24.cs1.a1', '24.cr1.a1', '24.cg1.a1', '24.ct1.a1', '24.cw1.a1', '24.cv1.a1', '24.db1.a1', '24.cy1.a1', '24.cx1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '40.b1.a1', '60.bh1.a1', '60.bn1.a1', '60.cc1.a1'], 'contains': ['240.b1.a1', '360.bm1.a1', '480.h1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [97, 6945, 66, 6764, 270, 2496, 686, 7489], 'generators': [11, 23, 5, 7], 'label': '2880.hl.120.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': ['24.d1.a1', '40.b1.a1'], 'normal_contains': ['240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '30.3', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536613
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1', '60.d1.a1', '60.e1.a1', '60.f1.a1', '60.bj1.a1'], 'contains': ['240.c1.a1', '240.d1.a1', '240.g1.a1', '240.u1.a1', '240.w1.a1', '240.ba1.a1', '240.bv1.a1', '360.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6263, -1, 6299, -1, 6520, -1, 6769, -1], 'generators': [127, 3669967, 1447, 7], 'label': '2880.hl.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536614
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '4.l1.a1'], 'contains': ['16.e1.a1', '16.h1.a1', '16.j1.a1', '24.cn1.a1', '24.cq1.a1', '40.l1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5791, -1, 6038, -1, 5225, -1, 2489, -1], 'generators': [11, 1440, 3669960, 5, 8025261, 50803200], 'label': '2880.hl.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536615
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '60.a1.a1', '60.g1.a1', '60.bk1.a1'], 'contains': ['240.c1.a1', '240.e1.a1', '240.i1.a1', '240.v1.a1', '240.bq1.a1', '360.b1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3836, -1, 3852, -1, 4090, -1, 4326, -1], 'generators': [1456, 5, 120, 16], 'label': '2880.hl.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536616
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '60.g1.a1', '60.h1.a1', '60.bj1.a1'], 'contains': ['240.c1.a1', '240.h1.a1', '240.k1.a1', '240.w1.a1', '240.bw1.a1', '360.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4737, -1, 4629, -1, 4295, -1, 3520, -1], 'generators': [127, 1447, 3669976, 7], 'label': '2880.hl.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536617
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '60.a1.a1', '60.h1.a1', '60.bl1.a1'], 'contains': ['240.c1.a1', '240.j1.a1', '240.l1.a1', '240.x1.a1', '240.bx1.a1', '360.d1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3471, -1, 3558, -1, 3830, -1, 4410, -1], 'generators': [1456, 3669965, 120, 16], 'label': '2880.hl.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536618
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '60.c1.a1', '60.h1.a1', '60.bk1.a1'], 'contains': ['240.c1.a1', '240.m1.a1', '240.n1.a1', '360.e1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [897, -1, 1165, -1, 1916, -1, 3409, -1], 'generators': [1456, 9, 120, 16], 'label': '2880.hl.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536619
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '60.c1.a1', '60.g1.a1', '60.bl1.a1'], 'contains': ['240.c1.a1', '240.o1.a1', '240.p1.a1', '360.f1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1674, -1, 1784, -1, 2226, -1, 3062, -1], 'generators': [1456, 3669969, 120, 16], 'label': '2880.hl.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536620
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '60.a1.a1', '60.i1.a1', '60.j1.a1', '60.k1.a1', '60.l1.a1', '60.m1.a1', '60.bm1.a1'], 'contains': ['240.d1.a1', '240.e1.a1', '240.j1.a1', '240.y1.a1', '240.bs1.a1', '360.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5758, -1, 5926, -1, 6214, -1, 6441, -1], 'generators': [3669960, 1456, 5, 16], 'label': '2880.hl.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536621
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '60.i1.a1', '60.n1.a1', '60.o1.a1', '60.p1.a1', '60.q1.a1', '60.r1.a1', '60.bj1.a1'], 'contains': ['240.d1.a1', '240.f1.a1', '240.k1.a1', '240.ba1.a1', '240.bw1.a1', '360.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6426, -1, 6605, -1, 6562, -1, 5542, -1], 'generators': [136, 3669967, 1447, 7], 'label': '2880.hl.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536622
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '60.a1.a1', '60.n1.a1', '60.s1.a1', '60.t1.a1', '60.u1.a1', '60.v1.a1', '60.bo1.a1'], 'contains': ['240.d1.a1', '240.i1.a1', '240.l1.a1', '240.bb1.a1', '240.ca1.a1', '360.i1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4516, -1, 5353, -1, 4819, -1, 6398, -1], 'generators': [23, 3669960, 122, 1463], 'label': '2880.hl.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536623
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '60.b1.a1', '60.j1.a1', '60.o1.a1', '60.s1.a1', '60.w1.a1', '60.x1.a1', '60.br1.a1'], 'contains': ['240.d1.a1', '240.be1.a1', '240.bf1.a1', '360.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7890, -1, 7910, -1, 8802, -1, 6726, -1], 'generators': [8025127, 3669967, 1447, 7], 'label': '2880.hl.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536624
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '60.c1.a1', '60.n1.a1', '60.w1.a1', '60.y1.a1', '60.z1.a1', '60.ba1.a1', '60.bm1.a1'], 'contains': ['240.d1.a1', '240.m1.a1', '240.o1.a1', '360.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1730, -1, 1891, -1, 3750, -1, 5365, -1], 'generators': [3669960, 1456, 9, 16], 'label': '2880.hl.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536625
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '4.l1.a1'], 'contains': ['16.f1.a1', '16.g1.a1', '16.j1.a1', '24.cv1.a1', '24.cz1.a1', '24.db1.a1', '40.m1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5827, -1, 5560, -1, 5743, -1, 2368, -1], 'generators': [1440, 8025132, 3669960, 8025242, 12, 50803200], 'label': '2880.hl.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536626
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '60.d1.a1', '60.k1.a1', '60.p1.a1', '60.t1.a1', '60.y1.a1', '60.bb1.a1', '60.br1.a1'], 'contains': ['240.d1.a1', '240.bf1.a1', '360.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9645, -1, 9587, -1, 9112, -1, 6652, -1], 'generators': [3669967, 8025136, 1447, 7], 'label': '2880.hl.120.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536627
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '60.b1.a1', '60.l1.a1', '60.p1.a1', '60.u1.a1', '60.z1.a1', '60.bc1.a1', '60.bs1.a1'], 'contains': ['240.d1.a1', '240.bg1.a1', '240.bi1.a1', '360.m1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9256, -1, 9398, -1, 9407, -1, 6165, -1], 'generators': [3669967, 1447, 8025247, 7], 'label': '2880.hl.120.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536628
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '60.c1.a1', '60.i1.a1', '60.x1.a1', '60.bb1.a1', '60.bc1.a1', '60.bd1.a1', '60.bo1.a1'], 'contains': ['240.d1.a1', '240.n1.a1', '240.p1.a1', '360.n1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1765, -1, 1943, -1, 3706, -1, 5321, -1], 'generators': [23, 3669960, 130, 1463], 'label': '2880.hl.120.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536629
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '60.e1.a1', '60.k1.a1', '60.q1.a1', '60.v1.a1', '60.w1.a1', '60.bc1.a1', '60.bt1.a1'], 'contains': ['240.d1.a1', '240.cb1.a1', '360.o1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6574, -1, 6946, -1, 8103, -1, 7047, -1], 'generators': [3669967, 1447, 8025137, 7], 'label': '2880.hl.120.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536630
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.r1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '60.f1.a1', '60.j1.a1', '60.r1.a1', '60.u1.a1', '60.y1.a1', '60.bd1.a1', '60.bt1.a1'], 'contains': ['240.d1.a1', '240.bh1.a1', '360.p1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8969, -1, 9338, -1, 8882, -1, 5868, -1], 'generators': [3669967, 1447, 8025126, 7], 'label': '2880.hl.120.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536631
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.s1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '60.d1.a1', '60.m1.a1', '60.o1.a1', '60.v1.a1', '60.ba1.a1', '60.bd1.a1', '60.bs1.a1'], 'contains': ['240.d1.a1', '240.bi1.a1', '360.q1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9412, -1, 9449, -1, 9493, -1, 7003, -1], 'generators': [8025256, 3669967, 1447, 7], 'label': '2880.hl.120.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536632
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.t1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '60.f1.a1', '60.l1.a1', '60.q1.a1', '60.s1.a1', '60.ba1.a1', '60.bb1.a1', '60.bu1.a1'], 'contains': ['240.d1.a1', '240.bj1.a1', '360.r1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8559, -1, 8975, -1, 8613, -1, 6355, -1], 'generators': [23, 3669960, 1463, 8025261], 'label': '2880.hl.120.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536633
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.u1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '60.e1.a1', '60.m1.a1', '60.r1.a1', '60.t1.a1', '60.x1.a1', '60.z1.a1', '60.bu1.a1'], 'contains': ['240.d1.a1', '240.cc1.a1', '360.s1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6781, -1, 6761, -1, 7852, -1, 6812, -1], 'generators': [23, 3669960, 1463, 8025253], 'label': '2880.hl.120.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536634
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '120.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '60.i1.a1', '60.be1.a1', '60.bk1.a1'], 'contains': ['240.e1.a1', '240.f1.a1', '240.n1.a1', '360.t1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3548, -1, 3592, -1, 3334, -1, 3281, -1], 'generators': [127, 1456, 5, 16], 'label': '2880.hl.120.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.v1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536635
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.w1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '60.a1.a1', '60.be1.a1', '60.cb1.a1'], 'contains': ['240.e1.a1', '240.g1.a1', '240.l1.a1', '240.br1.a1', '240.bt1.a1', '360.u1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3623, -1, 3926, -1, 4048, -1, 4368, -1], 'generators': [1456, 5, 3669856, 16], 'label': '2880.hl.120.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536636
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['1440.b1.a1', '1440.e1.a1', '1440.f1.a1', '1440.j1.a1', '1440.h1.a1', '1440.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.g1.a1', '4.i1.a1', '6.q1.a1', '6.r1.a1', '8.l1.a1', '10.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5889, 5596, 6065, 5753, 5231, 4657, 2329, 5343], 'generators': [11, 23, 3669967, 1456, 5, 8025253, 50803200, 7], 'label': '2880.hl.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.g1.a1', '4.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '2880.hl', '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': '2880.hl'}
  • id: 183536637
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '2880.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '4.l1.a1'], 'contains': ['16.f1.a1', '16.h1.a1', '16.i1.a1', '24.cx1.a1', '24.da1.a1', '40.n1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6055, -1, 6154, -1, 5406, -1, 2195, -1], 'generators': [1440, 3669960, 122, 12, 8025126, 50803200], 'label': '2880.hl.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536638
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '120.x1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '60.g1.a1', '60.be1.a1', '60.bm1.a1'], 'contains': ['240.e1.a1', '240.h1.a1', '240.o1.a1', '360.v1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3728, -1, 3637, -1, 3622, -1, 2927, -1], 'generators': [3669967, 1456, 5, 16], 'label': '2880.hl.120.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536639
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.y1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '60.g1.a1', '60.i1.a1', '60.cb1.a1'], 'contains': ['240.e1.a1', '240.k1.a1', '240.p1.a1', '360.w1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3801, -1, 3612, -1, 3359, -1, 3117, -1], 'generators': [1456, 5, 3669863, 16], 'label': '2880.hl.120.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.y1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536640
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.z1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '60.be1.a1', '60.bf1.a1', '60.bj1.a1'], 'contains': ['240.f1.a1', '240.g1.a1', '240.h1.a1', '240.bv1.a1', '240.bw1.a1', '360.x1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4687, -1, 4555, -1, 4253, -1, 3683, -1], 'generators': [136, 1447, 3669976, 7], 'label': '2880.hl.120.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.z1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536641
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '120.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '60.n1.a1', '60.bf1.a1', '60.bk1.a1'], 'contains': ['240.f1.a1', '240.i1.a1', '240.m1.a1', '360.y1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1315, -1, 2287, -1, 2857, -1, 3651, -1], 'generators': [127, 1456, 9, 16], 'label': '2880.hl.120.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536642
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bb1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '60.i1.a1', '60.bf1.a1', '60.bl1.a1'], 'contains': ['240.f1.a1', '240.j1.a1', '240.p1.a1', '360.z1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2954, -1, 2952, -1, 3310, -1, 3626, -1], 'generators': [127, 1456, 3669965, 16], 'label': '2880.hl.120.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536643
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bc1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '60.n1.a1', '60.be1.a1', '60.bl1.a1'], 'contains': ['240.f1.a1', '240.l1.a1', '240.o1.a1', '360.ba1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2314, -1, 3185, -1, 2942, -1, 3306, -1], 'generators': [127, 1456, 3669969, 16], 'label': '2880.hl.120.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536644
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.bd1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '60.a1.a1', '60.bf1.a1', '60.ce1.a1'], 'contains': ['240.g1.a1', '240.i1.a1', '240.j1.a1', '240.bz1.a1', '240.cd1.a1', '360.bb1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3504, -1, 3669, -1, 3871, -1, 4452, -1], 'generators': [1456, 3669856, 3669965, 16], 'label': '2880.hl.120.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536645
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.be1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '60.c1.a1', '60.bf1.a1', '60.cb1.a1'], 'contains': ['240.g1.a1', '240.m1.a1', '240.p1.a1', '360.bc1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1038, -1, 1754, -1, 1952, -1, 3559, -1], 'generators': [1456, 9, 3669856, 16], 'label': '2880.hl.120.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.be1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536646
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.bf1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '60.c1.a1', '60.be1.a1', '60.ce1.a1'], 'contains': ['240.g1.a1', '240.n1.a1', '240.o1.a1', '360.bd1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1339, -1, 1491, -1, 2033, -1, 3209, -1], 'generators': [1456, 3669856, 3669969, 16], 'label': '2880.hl.120.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536647
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bg1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '60.g1.a1', '60.bf1.a1', '60.bo1.a1'], 'contains': ['240.h1.a1', '240.i1.a1', '240.p1.a1', '360.be1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2295, -1, 2664, -1, 2665, -1, 3032, -1], 'generators': [23, 3669967, 122, 1463], 'label': '2880.hl.120.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536648
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1', '18.j1.a1', '18.k1.a1', '18.l1.a1', '18.m1.a1', '18.n1.a1', '18.o1.a1', '45.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7731, -1, 7652, -1, 7191, -1, 6218, -1], 'generators': [127, 23, 8023694, 5, 3669143, 50803200, 7], 'label': '2880.hl.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': '2880.hl', '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': '80.50'}
  • id: 183536649
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '120.bh1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '60.h1.a1', '60.bf1.a1', '60.bm1.a1'], 'contains': ['240.h1.a1', '240.j1.a1', '240.m1.a1', '360.bf1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2896, -1, 1528, -1, 3230, -1, 3373, -1], 'generators': [3669967, 1456, 9, 16], 'label': '2880.hl.120.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536650
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bi1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '60.h1.a1', '60.be1.a1', '60.bo1.a1'], 'contains': ['240.h1.a1', '240.l1.a1', '240.n1.a1', '360.bg1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2275, -1, 3165, -1, 2531, -1, 3093, -1], 'generators': [23, 3669967, 130, 1463], 'label': '2880.hl.120.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536651
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bj1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1.a1', '60.g1.a1', '60.n1.a1', '60.ce1.a1'], 'contains': ['240.i1.a1', '240.k1.a1', '240.o1.a1', '360.bh1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2806, -1, 2070, -1, 3163, -1, 3179, -1], 'generators': [1456, 3669863, 3669969, 16], 'label': '2880.hl.120.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536652
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bk1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1.a1', '60.h1.a1', '60.i1.a1', '60.ce1.a1'], 'contains': ['240.j1.a1', '240.k1.a1', '240.n1.a1', '360.bi1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2729, -1, 2554, -1, 3260, -1, 3440, -1], 'generators': [1456, 3669863, 3669965, 16], 'label': '2880.hl.120.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536653
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bl1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1.a1', '60.h1.a1', '60.n1.a1', '60.cb1.a1'], 'contains': ['240.k1.a1', '240.l1.a1', '240.m1.a1', '360.bj1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2109, -1, 3093, -1, 2351, -1, 3464, -1], 'generators': [1456, 9, 3669863, 16], 'label': '2880.hl.120.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536654
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '120.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '40.a1.a1', '60.bg1.a1', '60.bh1.a1', '60.bi1.a1'], 'contains': ['240.b1.a1', '360.bk1.a1', '480.c1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [315, -1, 116, -1, 16, -1, 913, -1], 'generators': [11, 124, 23, 7], 'label': '2880.hl.120.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536655
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.bn1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '60.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.d1.a1', '60.bj1.a1', '60.bm1.a1', '60.bo1.a1', '60.br1.a1', '60.bs1.a1', '60.bt1.a1', '60.bu1.a1'], 'contains': ['240.a1.a1', '240.d1.a1', '240.h1.a1', '360.bl1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5008, -1, 4850, -1, 5022, -1, 3248, -1], 'generators': [23, 3669967, 1456, 7], 'label': '2880.hl.120.bn1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536656
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '120.bo1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.d1.a1', '60.bg1.a1', '60.bn1.a1', '60.bp1.a1', '60.bv1.a1', '60.bw1.a1', '60.bx1.a1', '60.by1.a1'], 'contains': ['240.b1.a1', '360.bl1.a1', '480.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4104, -1, 4229, -1, 4484, -1, 1271, -1], 'generators': [11, 23, 3669143, 7], 'label': '2880.hl.120.bo1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536657
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '120.bp1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '40.d1.a1', '60.bq1.a1', '60.bz1.a1', '60.ca1.a1'], 'contains': ['240.q1.a1', '360.bl1.a1', '480.f1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4182, -1, 4341, -1, 4573, -1, 1390, -1], 'generators': [23, 1460, 3669964, 7], 'label': '2880.hl.120.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.f1.a1', 'old_label': '120.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536658
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '120.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '24.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '40.b1.a1', '60.bk1.a1', '60.bm1.a1', '60.cb1.a1'], 'contains': ['240.a1.a1', '240.e1.a1', '240.m1.a1', '360.bm1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [643, -1, 789, -1, 1660, -1, 2344, -1], 'generators': [23, 1456, 5, 7], 'label': '2880.hl.120.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536659
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '20.d1.a1', '20.e1.a1', '20.j1.a1', '20.k1.a1', '30.i1.a1', '30.l1.a1', '40.h1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [758, -1, 673, -1, 839, -1, 632, -1], 'generators': [11, 124, 23, 3669967, 1456, 5, 7], 'label': '2880.hl.10.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536660
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.br1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '40.e1.a1', '60.bg1.a1', '60.cc1.a1', '60.cd1.a1'], 'contains': ['240.b1.a1', '360.bn1.a1', '480.j1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [147, -1, 313, -1, 52, -1, 639, -1], 'generators': [11, 23, 3669848, 7], 'label': '2880.hl.120.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.br1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536661
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.bs1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '40.e1.a1', '60.bj1.a1', '60.cb1.a1', '60.ce1.a1'], 'contains': ['240.a1.a1', '240.g1.a1', '240.k1.a1', '360.bn1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1857, -1, 3138, -1, 2119, -1, 2304, -1], 'generators': [23, 1456, 3669863, 7], 'label': '2880.hl.120.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536662
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '120.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '40.c1.a1', '60.bk1.a1', '60.bo1.a1', '60.ce1.a1'], 'contains': ['240.a1.a1', '240.i1.a1', '240.n1.a1', '360.bo1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [690, -1, 987, -1, 1586, -1, 2411, -1], 'generators': [23, 122, 1456, 7], 'label': '2880.hl.120.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536663
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '120.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '40.c1.a1', '60.bh1.a1', '60.bp1.a1', '60.cd1.a1'], 'contains': ['240.b1.a1', '360.bo1.a1', '480.n1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [216, -1, 160, -1, 145, -1, 885, -1], 'generators': [11, 23, 122, 7], 'label': '2880.hl.120.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536664
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '120.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a1', '40.c1.a1', '60.bq1.a1'], 'contains': ['240.q1.a1', '360.bo1.a1', '480.o1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [245, -1, 229, -1, 289, -1, 1059, -1], 'generators': [23, 122, 1460, 7], 'label': '2880.hl.120.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '120.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536665
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '120.bw1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.5', 'aut_weyl_index': 360, 'centralizer': '120.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1.a1', '40.f1.a1', '60.bl1.a1', '60.bm1.a1', '60.ce1.a1'], 'contains': ['240.a1.a1', '240.j1.a1', '240.o1.a1', '360.bp1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [968, -1, 1036, -1, 1697, -1, 2380, -1], 'generators': [23, 1456, 3669969, 7], 'label': '2880.hl.120.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 183536666
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '120.bx1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '40.f1.a1', '60.bi1.a1', '60.bn1.a1', '60.cd1.a1'], 'contains': ['240.b1.a1', '360.bp1.a1', '480.q1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [390, -1, 262, -1, 164, -1, 809, -1], 'generators': [3669138, 11, 23, 7], 'label': '2880.hl.120.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536667
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.by1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.14', 'aut_weyl_index': 120, 'centralizer': '360.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '40.g1.a1', '60.bl1.a1', '60.bo1.a1', '60.cb1.a1'], 'contains': ['240.a1.a1', '240.l1.a1', '240.p1.a1', '360.bq1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [757, -1, 1434, -1, 1561, -1, 2271, -1], 'generators': [23, 1456, 3669850, 7], 'label': '2880.hl.120.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.by1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 183536668
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.bz1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '40.g1.a1', '60.bi1.a1', '60.bp1.a1', '60.cc1.a1'], 'contains': ['240.b1.a1', '360.bq1.a1', '480.t1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [276, -1, 362, -1, 116, -1, 667, -1], 'generators': [11, 23, 3669850, 7], 'label': '2880.hl.120.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536669
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '120.ca1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1.a1', '40.g1.a1', '60.bq1.a1'], 'contains': ['240.q1.a1', '360.bq1.a1', '480.u1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [349, -1, 420, -1, 251, -1, 1039, -1], 'generators': [23, 1460, 3669850, 7], 'label': '2880.hl.120.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.w1.a1', 'old_label': '120.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536670
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.f1.a1', '20.g1.a1', '30.j1.a1', '30.m1.a1', '40.i1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5331, -1, 5396, -1, 5154, -1, 1900, -1], 'generators': [11, 124, 23, 8025132, 3669967, 1456, 7], 'label': '2880.hl.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536671
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.cb1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.a1', '30.i1.a1', '40.h1.a1', '60.cf1.a1'], 'contains': ['240.r1.a1', '240.s1.a1', '240.t1.a1', '240.z1.a1', '240.bc1.a1', '240.bu1.a1', '240.by1.a1', '360.br1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2058, -1, 2420, -1, 1220, -1, 1146, -1], 'generators': [124, 5, 3669120, 3], 'label': '2880.hl.120.cb1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '120.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536672
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '120.cc1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '120.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.a1', '30.j1.a1', '40.i1.a1', '60.cf1.a1'], 'contains': ['240.r1.a1', '240.bk1.a1', '240.bl1.a1', '360.bs1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5817, -1, 6025, -1, 5732, -1, 1898, -1], 'generators': [3669120, 128, 8023692, 12], 'label': '2880.hl.120.cc1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '120.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536673
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.cd1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ce1.a1', '30.k1.a1', '40.j1.a1', '60.cf1.a1'], 'contains': ['240.r1.a1', '240.bm1.a1', '240.bn1.a1', '360.bu1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6359, -1, 6447, -1, 5940, -1, 1722, -1], 'generators': [8023681, 124, 3669120, 3], 'label': '2880.hl.120.cd1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '120.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536674
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.ce1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1.a1', '40.h1.a1', '60.a1.a1', '60.cg1.a1', '60.ch1.a1'], 'contains': ['240.u1.a1', '240.v1.a1', '240.x1.a1', '240.y1.a1', '240.bb1.a1', '240.br1.a1', '240.bz1.a1', '360.br1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4328, -1, 4512, -1, 4861, -1, 7609, -1], 'generators': [1440, 3669960, 5, 120], 'label': '2880.hl.120.ce1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.ce1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536675
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '120.cf1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '30.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '40.i1.a1', '60.b1.a1', '60.cg1.a1'], 'contains': ['240.u1.a1', '240.be1.a1', '240.bg1.a1', '360.bs1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8107, -1, 8186, -1, 8314, -1, 6205, -1], 'generators': [8025120, 1440, 3669960, 120], 'label': '2880.hl.120.cf1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.cf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536676
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '120.cg1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '60.b1.a1', '60.d1.a1', '60.ch1.a1'], 'contains': ['240.u1.a1', '240.bf1.a1', '240.bi1.a1', '360.bt1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9730, -1, 9808, -1, 9732, -1, 7525, -1], 'generators': [1440, 8025127, 3669960, 120], 'label': '2880.hl.120.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.cg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536677
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.ch1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a1', '40.j1.a1', '60.f1.a1', '60.cg1.a1', '60.ch1.a1'], 'contains': ['240.u1.a1', '240.bh1.a1', '240.bj1.a1', '360.bu1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8897, -1, 9289, -1, 8523, -1, 6241, -1], 'generators': [1440, 3669960, 120, 8025126], 'label': '2880.hl.120.ch1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.ch1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536678
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.ci1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '60.a1.a1'], 'contains': ['240.v1.a1', '240.w1.a1', '240.x1.a1', '240.bs1.a1', '240.bt1.a1', '240.ca1.a1', '240.cd1.a1', '360.bv1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5196, -1, 5201, -1, 5336, -1, 8486, -1], 'generators': [1440, 5, 3669976, 120], 'label': '2880.hl.120.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.ci1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536679
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.cj1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1.a1', '60.e1.a1'], 'contains': ['240.w1.a1', '240.cb1.a1', '240.cc1.a1', '360.bw1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6655, -1, 6873, -1, 7288, -1, 8985, -1], 'generators': [1440, 3669967, 8025137, 120], 'label': '2880.hl.120.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.cj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536680
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.ck1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '60.a1.a1', '60.ci1.a1', '60.cj1.a1'], 'contains': ['240.y1.a1', '240.ba1.a1', '240.bb1.a1', '240.bq1.a1', '240.bt1.a1', '240.bx1.a1', '240.cd1.a1', '360.bx1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5577, -1, 5662, -1, 5451, -1, 7840, -1], 'generators': [136, 1440, 3669960, 5], 'label': '2880.hl.120.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.ck1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536681
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.h1.a1', '20.i1.a1', '30.k1.a1', '30.n1.a1', '40.j1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6244, -1, 6290, -1, 5535, -1, 1721, -1], 'generators': [11, 124, 23, 3669967, 1456, 8025137, 7], 'label': '2880.hl.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536682
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.cl1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '40.k1.a1', '60.j1.a1', '60.cg1.a1', '60.ci1.a1'], 'contains': ['240.y1.a1', '240.be1.a1', '240.bh1.a1', '360.by1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7926, -1, 8388, -1, 8438, -1, 7169, -1], 'generators': [1440, 3669960, 5, 8025125], 'label': '2880.hl.120.cl1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536683
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '120.cm1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1.a1', '60.j1.a1', '60.ch1.a1', '60.cj1.a1'], 'contains': ['240.y1.a1', '240.bf1.a1', '240.bh1.a1', '360.bz1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9603, -1, 9726, -1, 9326, -1, 7761, -1], 'generators': [1440, 3669960, 5, 8025134], 'label': '2880.hl.120.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536684
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.cn1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '40.l1.a1', '60.l1.a1', '60.cg1.a1', '60.cj1.a1'], 'contains': ['240.y1.a1', '240.bg1.a1', '240.bj1.a1', '360.ca1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8452, -1, 8651, -1, 8482, -1, 7250, -1], 'generators': [1440, 3669960, 5, 8025245], 'label': '2880.hl.120.cn1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536685
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.co1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.a1', '60.l1.a1', '60.ch1.a1', '60.ci1.a1'], 'contains': ['240.y1.a1', '240.bi1.a1', '240.bj1.a1', '360.cb1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9455, -1, 9548, -1, 9156, -1, 7566, -1], 'generators': [1440, 3669960, 5, 8025254], 'label': '2880.hl.120.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.co1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.co1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536686
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '120.cp1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1.a1', '30.q1.a1', '40.k1.a1', '60.cf1.a1'], 'contains': ['240.z1.a1', '240.bk1.a1', '240.bm1.a1', '360.by1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6076, -1, 6141, -1, 5772, -1, 1591, -1], 'generators': [11, 5, 3669120, 8023686], 'label': '2880.hl.120.cp1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '120.cp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536687
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.cq1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1.a1', '30.r1.a1', '40.l1.a1', '60.cf1.a1'], 'contains': ['240.z1.a1', '240.bl1.a1', '240.bn1.a1', '360.ca1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6121, -1, 6210, -1, 5808, -1, 1682, -1], 'generators': [11, 5, 3669120, 8025261], 'label': '2880.hl.120.cq1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '120.cq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536688
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '120.cr1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '60.b1.a1', '60.o1.a1', '60.ci1.a1'], 'contains': ['240.ba1.a1', '240.be1.a1', '240.bi1.a1', '360.cc1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8411, -1, 8602, -1, 9534, -1, 7332, -1], 'generators': [127, 8025120, 1440, 3669960], 'label': '2880.hl.120.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.cr1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536689
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '120.cs1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '60.b1.a1', '60.p1.a1', '60.cj1.a1'], 'contains': ['240.ba1.a1', '240.bf1.a1', '240.bg1.a1', '360.cd1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9542, -1, 9482, -1, 9570, -1, 7648, -1], 'generators': [127, 1440, 8025127, 3669960], 'label': '2880.hl.120.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '120.cs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536690
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.ct1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.a1', '60.d1.a1', '60.o1.a1', '60.p1.a1'], 'contains': ['240.ba1.a1', '240.bf1.a1', '240.bi1.a1', '360.ce1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9678, -1, 9778, -1, 9810, -1, 7684, -1], 'generators': [127, 1440, 3669960, 8025136], 'label': '2880.hl.120.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.m1.a1', 'old_label': '120.ct1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536691
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.cu1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '60.f1.a1', '60.ci1.a1', '60.cj1.a1'], 'contains': ['240.ba1.a1', '240.bh1.a1', '240.bj1.a1', '360.cf1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8868, -1, 9259, -1, 8842, -1, 7368, -1], 'generators': [127, 1440, 3669960, 8025126], 'label': '2880.hl.120.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536692
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 60, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '5.a1.a1'], 'contains': ['20.d1.a1', '20.f1.a1', '20.h1.a1', '30.o1.a1', '30.q1.a1', '40.k1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5614, -1, 5670, -1, 5579, -1, 1527, -1], 'generators': [11, 23, 3669967, 1456, 5, 8025137, 7], 'label': '2880.hl.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 183536693
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.cv1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1.a1', '40.m1.a1', '60.s1.a1', '60.cg1.a1', '60.ci1.a1'], 'contains': ['240.bb1.a1', '240.be1.a1', '240.bj1.a1', '360.cg1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8217, -1, 8314, -1, 8278, -1, 7209, -1], 'generators': [8025120, 1440, 3669960, 8025261], 'label': '2880.hl.120.cv1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536694
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.cw1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1.a1', '60.s1.a1', '60.ch1.a1', '60.cj1.a1'], 'contains': ['240.bb1.a1', '240.bf1.a1', '240.bj1.a1', '360.ch1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9570, -1, 9693, -1, 9072, -1, 7721, -1], 'generators': [1440, 3669960, 8025143, 8025261], 'label': '2880.hl.120.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536695
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.cx1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1.a1', '40.n1.a1', '60.u1.a1', '60.cg1.a1', '60.cj1.a1'], 'contains': ['240.bb1.a1', '240.bg1.a1', '240.bh1.a1', '360.ci1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8733, -1, 9024, -1, 8653, -1, 7129, -1], 'generators': [1440, 3669960, 122, 8025122], 'label': '2880.hl.120.cx1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536696
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.cy1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1.a1', '60.u1.a1', '60.ch1.a1', '60.ci1.a1'], 'contains': ['240.bb1.a1', '240.bh1.a1', '240.bi1.a1', '360.cj1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9488, -1, 9660, -1, 9366, -1, 7489, -1], 'generators': [1440, 3669960, 122, 8025141], 'label': '2880.hl.120.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.cy1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536697
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.cz1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1.a1', '30.u1.a1', '40.m1.a1', '60.cf1.a1'], 'contains': ['240.bc1.a1', '240.bk1.a1', '240.bn1.a1', '360.cg1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6043, -1, 6103, -1, 5537, -1, 1763, -1], 'generators': [8025242, 3669120, 8023692, 12], 'label': '2880.hl.120.cz1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '120.cz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536698
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '120.da1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1.a1', '30.v1.a1', '40.n1.a1', '60.cf1.a1'], 'contains': ['240.bc1.a1', '240.bl1.a1', '240.bm1.a1', '360.ci1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6215, -1, 6331, -1, 5980, -1, 1554, -1], 'generators': [122, 3669120, 8023686, 12], 'label': '2880.hl.120.da1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '120.da1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.da1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536699
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '120.db1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1.a1', '30.w1.a1', '40.m1.a1'], 'contains': ['240.bd1.a1', '240.bo1.a1', '240.bp1.a1', '360.cg1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [6186, -1, 6181, -1, 6410, -1, 1948, -1], 'generators': [8025132, 1452, 8025242, 3669968], 'label': '2880.hl.120.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.db1.a1', 'old_label': '120.db1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.db1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536700
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.dc1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1.a1', '60.a1.a1'], 'contains': ['240.bq1.a1', '240.br1.a1', '240.bs1.a1', '240.bv1.a1', '240.bx1.a1', '240.bz1.a1', '240.ca1.a1', '360.ck1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5229, -1, 5469, -1, 5294, -1, 8444, -1], 'generators': [136, 1440, 5, 3669976], 'label': '2880.hl.120.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '120.dc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536701
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '120.dd1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1.a1', '60.e1.a1'], 'contains': ['240.bv1.a1', '240.cb1.a1', '240.cc1.a1', '360.cl1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6684, -1, 6843, -1, 7252, -1, 8949, -1], 'generators': [127, 1440, 3669967, 8025137], 'label': '2880.hl.120.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.dd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536702
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '144.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '24.5', 'aut_weyl_index': 120, 'centralizer': '24.a1.a1', 'complements': ['20.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.t1.a1', '72.a1.a1', '72.bl1.a1', '72.bm1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '72.bq1.a1'], 'contains': ['288.b1.a1', '720.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1227, 4806, 934, 4789, 936, 4288, 2738, 5696], 'generators': [23, 50803200, 7], 'label': '2880.hl.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.b1.a1', '72.a1.a1'], 'normal_contains': ['576.a1.a1', '720.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '24.5', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 183536703
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '10.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '5.a1.a1'], 'contains': ['20.d1.a1', '20.g1.a1', '20.i1.a1', '30.p1.a1', '30.r1.a1', '40.l1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5951, -1, 6009, -1, 5235, -1, 1620, -1], 'generators': [11, 23, 3669967, 1456, 5, 8025253, 7], 'label': '2880.hl.10.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536704
    {'ambient': '2880.hl', 'aut_centralizer_order': 144, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '20.a1.a1', 'complements': ['20.a1.a1', '20.c1.a1', '20.k1.a1', '20.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.bk1.a1', '48.bo1.a1', '72.k1.a1', '72.bs1.a1', '72.by1.a1', '72.cc1.a1', '72.cg1.a1'], 'contains': ['288.a1.a1', '720.w1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8044, 1842, 7834, 1861, 6788, 7636, 7752, 2349], 'generators': [3669120, 8023680, 50803200], 'label': '2880.hl.144.b1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['36.a1.a1', '48.d1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '1.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536705
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1', '72.bl1.a1'], 'contains': ['288.b1.a1', '288.c1.a1', '288.e1.a1', '720.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3358, -1, 3177, -1, 3044, -1, 4987, -1], 'generators': [127, 50803200, 7], 'label': '2880.hl.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536706
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.a1.a1', '72.b1.a1', '72.h1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1'], 'contains': ['288.a1.a1', '288.b1.a1', '288.g1.a1', '720.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7307, -1, 6664, -1, 6462, -1, 7730, -1], 'generators': [3669120, 50803200, 7], 'label': '2880.hl.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.d1.a1', 'projective_image': '2880.hl', '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': '20.3'}
  • id: 183536707
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '72.c1.a1', '72.h1.a1', '72.u1.a1', '72.v1.a1', '72.w1.a1', '72.x1.a1', '72.bm1.a1'], 'contains': ['288.b1.a1', '288.d1.a1', '720.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3743, -1, 4104, -1, 3383, -1, 4543, -1], 'generators': [5, 50803200, 16], 'label': '2880.hl.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536708
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '72.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '72.i1.a1', '72.u1.a1', '72.y1.a1', '72.z1.a1', '72.ba1.a1', '72.bb1.a1', '72.bl1.a1'], 'contains': ['288.b1.a1', '288.e1.a1', '720.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3912, -1, 4044, -1, 3211, -1, 4636, -1], 'generators': [136, 50803200, 7], 'label': '2880.hl.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536709
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '72.b1.a1', '72.v1.a1', '72.y1.a1', '72.bc1.a1', '72.bd1.a1', '72.be1.a1', '72.bn1.a1'], 'contains': ['288.b1.a1', '288.f1.a1', '288.j1.a1', '720.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3314, -1, 3251, -1, 3266, -1, 5037, -1], 'generators': [3669840, 50803200, 7], 'label': '2880.hl.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536710
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '72.a1.a1', '72.d1.a1', '72.w1.a1', '72.y1.a1', '72.bf1.a1', '72.bg1.a1', '72.bh1.a1'], 'contains': ['288.b1.a1', '288.g1.a1', '720.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4593, -1, 4585, -1, 3656, -1, 4670, -1], 'generators': [3669143, 50803200, 7], 'label': '2880.hl.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536711
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '72.c1.a1', '72.j1.a1', '72.z1.a1', '72.bc1.a1', '72.bf1.a1', '72.bi1.a1', '72.bo1.a1'], 'contains': ['288.b1.a1', '288.h1.a1', '720.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3214, -1, 2825, -1, 2942, -1, 4751, -1], 'generators': [23, 122, 50803200], 'label': '2880.hl.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536712
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '72.e1.a1', '72.h1.a1', '72.ba1.a1', '72.bc1.a1', '72.bg1.a1', '72.bj1.a1', '72.bp1.a1'], 'contains': ['288.b1.a1', '288.i1.a1', '720.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3171, -1, 2639, -1, 3116, -1, 5061, -1], 'generators': [3669134, 50803200, 16], 'label': '2880.hl.144.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536713
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '72.d1.a1', '72.i1.a1', '72.x1.a1', '72.bi1.a1', '72.bj1.a1', '72.bk1.a1', '72.bn1.a1'], 'contains': ['288.b1.a1', '288.j1.a1', '720.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3844, -1, 3964, -1, 3290, -1, 4485, -1], 'generators': [3669863, 50803200, 7], 'label': '2880.hl.144.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536714
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '10.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '5.a1.a1'], 'contains': ['20.e1.a1', '20.f1.a1', '20.i1.a1', '30.s1.a1', '30.u1.a1', '30.w1.a1', '40.m1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5907, -1, 5634, -1, 5707, -1, 1777, -1], 'generators': [11, 23, 8025132, 3669967, 1456, 8025253, 7], 'label': '2880.hl.10.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.f1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536715
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '72.e1.a1', '72.j1.a1', '72.v1.a1', '72.bb1.a1', '72.bh1.a1', '72.bk1.a1', '72.bq1.a1'], 'contains': ['288.b1.a1', '288.k1.a1', '720.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3086, -1, 2927, -1, 2698, -1, 4718, -1], 'generators': [23, 3669842, 50803200], 'label': '2880.hl.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536716
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '24.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '72.f1.a1', '72.l1.a1', '72.z1.a1', '72.bd1.a1', '72.bg1.a1', '72.bk1.a1', '72.bm1.a1'], 'contains': ['288.b1.a1', '720.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1270, -1, 1211, -1, 1910, -1, 4589, -1], 'generators': [9, 50803200, 16], 'label': '2880.hl.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536717
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '72.f1.a1', '72.o1.a1', '72.u1.a1', '72.be1.a1', '72.bh1.a1', '72.bj1.a1', '72.bo1.a1'], 'contains': ['288.b1.a1', '720.m1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1534, -1, 1288, -1, 1993, -1, 4109, -1], 'generators': [23, 130, 50803200], 'label': '2880.hl.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536718
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '72.g1.a1', '72.l1.a1', '72.w1.a1', '72.bb1.a1', '72.be1.a1', '72.bi1.a1', '72.bp1.a1'], 'contains': ['288.b1.a1', '720.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1580, -1, 1308, -1, 2312, -1, 3914, -1], 'generators': [3669138, 50803200, 16], 'label': '2880.hl.144.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536719
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 72, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '72.g1.a1', '72.o1.a1', '72.x1.a1', '72.ba1.a1', '72.bd1.a1', '72.bf1.a1', '72.bq1.a1'], 'contains': ['288.b1.a1', '720.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1560, -1, 1664, -1, 2283, -1, 4085, -1], 'generators': [23, 3669850, 50803200], 'label': '2880.hl.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 183536720
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.u1.a1', '72.b1.a1', '72.br1.a1', '72.bs1.a1', '72.bt1.a1', '72.bu1.a1'], 'contains': ['288.a1.a1', '288.c1.a1', '288.f1.a1', '720.p1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4282, -1, 3816, -1, 4945, -1, 7929, -1], 'generators': [3669120, 120, 50803200], 'label': '2880.hl.144.q1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536721
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.a1', '48.x1.a1', '72.c1.a1', '72.br1.a1', '72.bv1.a1'], 'contains': ['288.c1.a1', '288.d1.a1', '288.h1.a1', '720.q1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4152, -1, 3476, -1, 4289, -1, 8374, -1], 'generators': [5, 120, 50803200], 'label': '2880.hl.144.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536722
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1.a1', '72.b1.a1', '72.d1.a1', '72.bv1.a1', '72.bw1.a1'], 'contains': ['288.c1.a1', '288.g1.a1', '288.j1.a1', '720.r1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5816, -1, 5722, -1, 5645, -1, 8637, -1], 'generators': [3669143, 120, 50803200], 'label': '2880.hl.144.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536723
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '48.z1.a1', '72.e1.a1', '72.br1.a1', '72.bv1.a1'], 'contains': ['288.c1.a1', '288.i1.a1', '288.k1.a1', '720.s1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4546, -1, 4362, -1, 4208, -1, 8492, -1], 'generators': [3669125, 120, 50803200], 'label': '2880.hl.144.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536724
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1.a1', '48.bb1.a1', '72.h1.a1', '72.br1.a1', '72.bx1.a1', '72.by1.a1', '72.bz1.a1', '72.ca1.a1', '72.cb1.a1'], 'contains': ['288.a1.a1', '288.d1.a1', '288.i1.a1', '720.t1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5527, -1, 5620, -1, 5524, -1, 8408, -1], 'generators': [5, 3669120, 50803200], 'label': '2880.hl.144.u1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536725
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '10.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '144.183', 'aut_weyl_index': 20, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '5.a1.a1'], 'contains': ['20.e1.a1', '20.g1.a1', '20.h1.a1', '30.t1.a1', '30.v1.a1', '40.n1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6042, -1, 6108, -1, 5371, -1, 1461, -1], 'generators': [11, 23, 3669967, 122, 1456, 8025137, 7], 'label': '2880.hl.10.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 183536726
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '72.b1.a1', '72.i1.a1', '72.bx1.a1', '72.cc1.a1', '72.cd1.a1', '72.ce1.a1', '72.cf1.a1'], 'contains': ['288.a1.a1', '288.e1.a1', '288.j1.a1', '720.u1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6473, -1, 6684, -1, 6327, -1, 8115, -1], 'generators': [136, 3669120, 50803200], 'label': '2880.hl.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536727
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1.a1', '48.be1.a1', '48.bf1.a1', '72.j1.a1', '72.br1.a1', '72.bx1.a1', '72.cg1.a1', '72.ch1.a1', '72.ci1.a1', '72.cj1.a1'], 'contains': ['288.a1.a1', '288.h1.a1', '288.k1.a1', '720.v1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4908, -1, 5144, -1, 4968, -1, 8091, -1], 'generators': [122, 3669120, 50803200], 'label': '2880.hl.144.w1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536728
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1.a1', '72.k1.a1', '72.m1.a1', '72.bt1.a1', '72.bz1.a1', '72.cd1.a1', '72.ce1.a1', '72.ch1.a1'], 'contains': ['288.a1.a1', '720.x1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9050, -1, 8795, -1, 7595, -1, 8137, -1], 'generators': [3669120, 8023696, 50803200], 'label': '2880.hl.144.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536729
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.bl1.a1', '72.n1.a1', '72.bs1.a1', '72.ca1.a1', '72.cd1.a1', '72.ci1.a1'], 'contains': ['288.a1.a1', '720.y1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8692, -1, 8473, -1, 6896, -1, 7771, -1], 'generators': [3669120, 8025240, 50803200], 'label': '2880.hl.144.y1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536730
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.a1', '48.bm1.a1', '72.q1.a1', '72.bu1.a1', '72.by1.a1', '72.bz1.a1', '72.cf1.a1', '72.ci1.a1', '72.cj1.a1'], 'contains': ['288.a1.a1', '720.z1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8953, -1, 8711, -1, 6915, -1, 7950, -1], 'generators': [3669120, 8023686, 50803200], 'label': '2880.hl.144.z1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536731
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1.a1', '72.n1.a1', '72.r1.a1', '72.bt1.a1', '72.cb1.a1', '72.cc1.a1', '72.ce1.a1', '72.cj1.a1'], 'contains': ['288.a1.a1', '720.ba1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8977, -1, 8810, -1, 7658, -1, 8047, -1], 'generators': [8025256, 3669120, 50803200], 'label': '2880.hl.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536732
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1.a1', '48.bn1.a1', '48.bp1.a1', '72.s1.a1', '72.bu1.a1', '72.ca1.a1', '72.cb1.a1', '72.cf1.a1', '72.cg1.a1', '72.ch1.a1'], 'contains': ['288.a1.a1', '720.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8779, -1, 8504, -1, 6877, -1, 7791, -1], 'generators': [3669120, 8025261, 50803200], 'label': '2880.hl.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536733
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1.a1', '72.c1.a1', '72.bx1.a1', '72.ck1.a1'], 'contains': ['288.d1.a1', '288.e1.a1', '288.h1.a1', '720.bc1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5366, -1, 5265, -1, 4850, -1, 8831, -1], 'generators': [136, 5, 50803200], 'label': '2880.hl.144.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536734
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a1', '48.bu1.a1', '72.v1.a1', '72.br1.a1', '72.ck1.a1'], 'contains': ['288.d1.a1', '288.f1.a1', '288.k1.a1', '720.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4566, -1, 4749, -1, 4231, -1, 8340, -1], 'generators': [5, 3669840, 50803200], 'label': '2880.hl.144.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536735
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '72.h1.a1', '72.bv1.a1', '72.ck1.a1'], 'contains': ['288.d1.a1', '288.g1.a1', '288.i1.a1', '720.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5459, -1, 5506, -1, 5198, -1, 8960, -1], 'generators': [5, 3669136, 50803200], 'label': '2880.hl.144.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536736
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '720.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.n1.a1', '6.o1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.e1.a1', '24.h1.a1', '24.j1.a1', '24.o1.a1', '24.be1.a1', '36.bh1.a1', '60.bj1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4587, 3292, 4163, 2699, 4171, 6845, 4633, 3155], 'generators': [127, 23, 3669967, 1456, 50803200, 7], 'label': '2880.hl.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.e1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536737
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '72.v1.a1', '72.bv1.a1', '72.bx1.a1'], 'contains': ['288.d1.a1', '288.j1.a1', '288.k1.a1', '720.bf1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5290, -1, 5221, -1, 4884, -1, 8888, -1], 'generators': [5, 3669856, 50803200], 'label': '2880.hl.144.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536738
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1.a1', '72.b1.a1', '72.y1.a1', '72.ck1.a1', '72.cl1.a1'], 'contains': ['288.e1.a1', '288.f1.a1', '288.g1.a1', '720.bg1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5887, -1, 5741, -1, 5621, -1, 8576, -1], 'generators': [143, 3669143, 50803200], 'label': '2880.hl.144.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536739
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '72.d1.a1', '72.i1.a1', '72.y1.a1'], 'contains': ['288.e1.a1', '288.g1.a1', '288.j1.a1', '720.bh1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5859, -1, 5584, -1, 5260, -1, 6572, -1], 'generators': [127, 3669143, 50803200], 'label': '2880.hl.144.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '144.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536740
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '72.e1.a1', '72.bx1.a1', '72.ck1.a1'], 'contains': ['288.e1.a1', '288.i1.a1', '288.k1.a1', '720.bi1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5060, -1, 4993, -1, 4737, -1, 8864, -1], 'generators': [136, 3669125, 50803200], 'label': '2880.hl.144.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536741
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '48.bz1.a1', '72.bc1.a1', '72.br1.a1', '72.ck1.a1'], 'contains': ['288.f1.a1', '288.h1.a1', '288.i1.a1', '720.bj1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4004, -1, 4000, -1, 4255, -1, 8468, -1], 'generators': [3669125, 3669840, 50803200], 'label': '2880.hl.144.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536742
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1.a1', '72.j1.a1', '72.bv1.a1', '72.ck1.a1'], 'contains': ['288.g1.a1', '288.h1.a1', '288.k1.a1', '720.bk1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4794, -1, 5013, -1, 4713, -1, 8936, -1], 'generators': [122, 3669143, 50803200], 'label': '2880.hl.144.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536743
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1.a1', '72.p1.a1', '72.bw1.a1', '72.cl1.a1'], 'contains': ['288.g1.a1', '720.bl1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6523, -1, 6501, -1, 6675, -1, 8659, -1], 'generators': [8023697, 3669127, 50803200], 'label': '2880.hl.144.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '144.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536744
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.a1', '72.t1.a1', '72.bw1.a1', '72.cl1.a1'], 'contains': ['288.g1.a1', '720.bm1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6538, -1, 6517, -1, 6647, -1, 8678, -1], 'generators': [8025253, 3669143, 50803200], 'label': '2880.hl.144.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '144.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536745
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1.a1', '72.bc1.a1', '72.bv1.a1', '72.bx1.a1'], 'contains': ['288.h1.a1', '288.i1.a1', '288.j1.a1', '720.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4976, -1, 4508, -1, 4761, -1, 8912, -1], 'generators': [3669125, 3669856, 50803200], 'label': '2880.hl.144.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536746
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '48.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '40.a1.a1', '80.b1.a1', '80.c1.a1', '80.d1.a1'], 'contains': ['320.a1.a1', '480.a1.a1', '480.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [809, -1, 567, -1, 714, -1, 549, -1], 'generators': [124, 1440, 3], 'label': '2880.hl.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '160.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536747
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['1440.d1.a1', '1440.i1.a1', '1440.b1.a1', '1440.e1.a1', '1440.f1.a1', '1440.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.a1', '4.i1.a1', '6.s1.a1', '6.u1.a1', '6.w1.a1', '8.m1.a1', '10.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5841, 2620, 5584, 4814, 5707, 3788, 2259, 6213], 'generators': [11, 23, 8025132, 3669967, 1456, 8025253, 50803200, 7], 'label': '2880.hl.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.a1', '4.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536748
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.k1.a1', '6.r1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '36.bk1.a1', '48.bb1.a1', '60.bn1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3231, 4937, 1285, 5334, 2205, 4942, 1265, 5058], 'generators': [11, 23, 5, 3669143, 50803200, 7], 'label': '2880.hl.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1'], 'normal_contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '2880.hl', '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': '480.1189'}
  • id: 183536749
    {'ambient': '2880.hl', 'aut_centralizer_order': 36, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '80.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '40.d1.a1', '80.b1.a1', '80.e1.a1', '80.f1.a1', '80.g1.a1', '80.h1.a1', '80.i1.a1', '80.j1.a1'], 'contains': ['320.a1.a1', '480.d1.a1', '480.e1.a1', '480.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [4237, -1, 4289, -1, 4683, -1, 1514, -1], 'generators': [11, 1440, 3669960], 'label': '2880.hl.160.b1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '160.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536750
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '40.b1.a1', '80.c1.a1', '80.e1.a1', '80.k1.a1'], 'contains': ['320.a1.a1', '480.g1.a1', '480.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2471, -1, 2855, -1, 1475, -1, 406, -1], 'generators': [11, 1440, 5], 'label': '2880.hl.160.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '160.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536751
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '40.e1.a1', '80.b1.a1', '80.k1.a1', '80.l1.a1'], 'contains': ['320.a1.a1', '480.j1.a1', '480.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [767, -1, 604, -1, 857, -1, 307, -1], 'generators': [1440, 12, 3669848], 'label': '2880.hl.160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '160.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536752
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '40.c1.a1', '80.c1.a1', '80.f1.a1', '80.l1.a1'], 'contains': ['320.a1.a1', '480.m1.a1', '480.n1.a1', '480.o1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [941, -1, 1022, -1, 1353, -1, 518, -1], 'generators': [1440, 122, 12], 'label': '2880.hl.160.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '160.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536753
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '160.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '240.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '40.f1.a1', '80.d1.a1', '80.e1.a1', '80.l1.a1'], 'contains': ['320.a1.a1', '480.p1.a1', '480.q1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1479, -1, 1055, -1, 1287, -1, 488, -1], 'generators': [1440, 3669974, 12], 'label': '2880.hl.160.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '160.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536754
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '160.g1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '36.10', 'aut_weyl_index': 80, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '40.g1.a1', '80.d1.a1', '80.f1.a1', '80.k1.a1'], 'contains': ['320.a1.a1', '480.s1.a1', '480.t1.a1', '480.u1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1147, -1, 2139, -1, 1170, -1, 458, -1], 'generators': [1440, 3669842, 12], 'label': '2880.hl.160.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '160.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 183536755
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.a1.a1', '90.a1.a1', '90.b1.a1', '90.i1.a1'], 'contains': ['360.a1.a1', '360.b1.a1', '360.d1.a1', '360.g1.a1', '360.i1.a1', '360.u1.a1', '360.bb1.a1', '360.br1.a1', '360.bv1.a1', '360.bx1.a1', '360.ck1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4481, -1, 5089, -1, 4751, -1, 6546, -1], 'generators': [5, 3669136, 120, 16], 'label': '2880.hl.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536756
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.b1.a1', '90.a1.a1', '90.c1.a1', '90.j1.a1'], 'contains': ['360.a1.a1', '360.j1.a1', '360.m1.a1', '360.bs1.a1', '360.bt1.a1', '360.cc1.a1', '360.cd1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8451, -1, 8645, -1, 9609, -1, 6079, -1], 'generators': [127, 3669120, 8023687, 7], 'label': '2880.hl.180.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536757
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.c1.a1', '90.c1.a1', '90.d1.a1', '90.i1.a1'], 'contains': ['360.a1.a1', '360.e1.a1', '360.f1.a1', '360.k1.a1', '360.n1.a1', '360.bc1.a1', '360.bd1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1464, -1, 1539, -1, 1829, -1, 4855, -1], 'generators': [9, 3669136, 120, 16], 'label': '2880.hl.180.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536758
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '60.d1.a1', '90.b1.a1', '90.d1.a1', '90.j1.a1'], 'contains': ['360.a1.a1', '360.l1.a1', '360.q1.a1', '360.bt1.a1', '360.ce1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9552, -1, 9642, -1, 9771, -1, 6959, -1], 'generators': [127, 3669120, 8023696, 7], 'label': '2880.hl.180.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536759
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '240.a1.a1', 'complements': ['240.s1.a1', '240.t1.a1', '240.by1.a1', '240.bu1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.p1.a1', '6.s1.a1'], 'contains': ['24.b1.a1', '24.q1.a1', '24.s1.a1', '36.a1.a1', '60.br1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8066, 1000, 8146, 973, 6668, 8970, 5886, 1033], 'generators': [23, 3669967, 8025136, 1456, 50803200, 7], 'label': '2880.hl.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536760
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '60.e1.a1', '90.b1.a1', '90.c1.a1', '90.k1.a1'], 'contains': ['360.a1.a1', '360.o1.a1', '360.s1.a1', '360.bw1.a1', '360.cl1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6952, -1, 7087, -1, 7895, -1, 7090, -1], 'generators': [127, 8023697, 3669120, 7], 'label': '2880.hl.180.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536761
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '60.f1.a1', '90.a1.a1', '90.d1.a1', '90.k1.a1'], 'contains': ['360.a1.a1', '360.p1.a1', '360.r1.a1', '360.bu1.a1', '360.cf1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9201, -1, 9453, -1, 8759, -1, 5782, -1], 'generators': [127, 3669120, 8023686, 7], 'label': '2880.hl.180.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536762
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '60.g1.a1', '90.i1.a1'], 'contains': ['360.b1.a1', '360.c1.a1', '360.f1.a1', '360.v1.a1', '360.w1.a1', '360.be1.a1', '360.bh1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2877, -1, 2881, -1, 2887, -1, 3001, -1], 'generators': [5, 3669143, 120, 16], 'label': '2880.hl.180.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536763
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '60.h1.a1', '90.i1.a1'], 'contains': ['360.c1.a1', '360.d1.a1', '360.e1.a1', '360.bf1.a1', '360.bg1.a1', '360.bi1.a1', '360.bj1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2367, -1, 2461, -1, 2391, -1, 3336, -1], 'generators': [9, 3669143, 120, 16], 'label': '2880.hl.180.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536764
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '60.i1.a1', '90.e1.a1', '90.f1.a1', '90.i1.a1'], 'contains': ['360.g1.a1', '360.h1.a1', '360.n1.a1', '360.t1.a1', '360.w1.a1', '360.z1.a1', '360.bi1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3280, -1, 3292, -1, 3790, -1, 4894, -1], 'generators': [127, 5, 3669136, 16], 'label': '2880.hl.180.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536765
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '60.j1.a1', '90.a1.a1', '90.e1.a1', '90.l1.a1'], 'contains': ['360.g1.a1', '360.j1.a1', '360.p1.a1', '360.by1.a1', '360.bz1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8301, -1, 8483, -1, 8924, -1, 5953, -1], 'generators': [8023694, 5, 3669136, 16], 'label': '2880.hl.180.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536766
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '60.k1.a1', '90.b1.a1', '90.f1.a1', '90.l1.a1'], 'contains': ['360.g1.a1', '360.l1.a1', '360.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7075, -1, 7860, -1, 8193, -1, 6850, -1], 'generators': [5, 8023698, 3669136, 16], 'label': '2880.hl.180.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536767
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1.a1', '60.l1.a1', '90.a1.a1', '90.f1.a1', '90.m1.a1'], 'contains': ['360.g1.a1', '360.m1.a1', '360.r1.a1', '360.ca1.a1', '360.cb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8835, -1, 9041, -1, 9033, -1, 5995, -1], 'generators': [5, 8025254, 3669136, 16], 'label': '2880.hl.180.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536768
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1.a1', '60.m1.a1', '90.b1.a1', '90.e1.a1', '90.m1.a1'], 'contains': ['360.g1.a1', '360.q1.a1', '360.s1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7592, -1, 7302, -1, 8067, -1, 6689, -1], 'generators': [5, 8025258, 3669136, 16], 'label': '2880.hl.180.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536769
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.n1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1.a1', '60.n1.a1', '90.g1.a1', '90.h1.a1', '90.i1.a1'], 'contains': ['360.h1.a1', '360.i1.a1', '360.k1.a1', '360.y1.a1', '360.ba1.a1', '360.bh1.a1', '360.bj1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2245, -1, 2624, -1, 3046, -1, 4931, -1], 'generators': [127, 9, 3669136, 16], 'label': '2880.hl.180.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536770
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '720.783', 'aut_weyl_index': 4, 'centralizer': '720.a1.a1', 'complements': ['240.s1.a1', '240.bu1.a1', '240.t1.a1', '240.by1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.a1.a1', '6.q1.a1', '6.t1.a1'], 'contains': ['24.b1.a1', '24.t1.a1', '24.x1.a1', '36.bm1.a1', '60.bs1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8942, 1842, 9187, 1814, 7963, 8191, 5940, 1813], 'generators': [8025256, 23, 3669967, 1456, 50803200, 7], 'label': '2880.hl.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.g1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '720.783'}
  • id: 183536771
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.o1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '60.o1.a1', '90.e1.a1', '90.g1.a1', '90.j1.a1'], 'contains': ['360.h1.a1', '360.j1.a1', '360.q1.a1', '360.cc1.a1', '360.ce1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8380, -1, 8550, -1, 9651, -1, 6609, -1], 'generators': [136, 3669120, 8023687, 7], 'label': '2880.hl.180.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536772
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.p1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '60.p1.a1', '90.f1.a1', '90.h1.a1', '90.j1.a1'], 'contains': ['360.h1.a1', '360.l1.a1', '360.m1.a1', '360.cd1.a1', '360.ce1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9244, -1, 9486, -1, 9693, -1, 5911, -1], 'generators': [136, 3669120, 8023696, 7], 'label': '2880.hl.180.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536773
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.q1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '60.q1.a1', '90.f1.a1', '90.g1.a1', '90.k1.a1'], 'contains': ['360.h1.a1', '360.o1.a1', '360.r1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7380, -1, 7794, -1, 8140, -1, 5746, -1], 'generators': [136, 8023697, 3669120, 7], 'label': '2880.hl.180.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536774
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.r1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1.a1', '60.r1.a1', '90.e1.a1', '90.h1.a1', '90.k1.a1'], 'contains': ['360.h1.a1', '360.p1.a1', '360.s1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7767, -1, 7425, -1, 8036, -1, 5625, -1], 'generators': [136, 3669120, 8023686, 7], 'label': '2880.hl.180.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536775
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.s1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '60.s1.a1', '90.a1.a1', '90.g1.a1', '90.n1.a1'], 'contains': ['360.i1.a1', '360.j1.a1', '360.r1.a1', '360.cg1.a1', '360.ch1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8346, -1, 8274, -1, 8692, -1, 6037, -1], 'generators': [8023703, 23, 8025261, 3669143], 'label': '2880.hl.180.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536776
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.t1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '60.t1.a1', '90.b1.a1', '90.h1.a1', '90.n1.a1'], 'contains': ['360.i1.a1', '360.l1.a1', '360.s1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7625, -1, 7240, -1, 8006, -1, 6573, -1], 'generators': [23, 8025253, 3669143, 8023696], 'label': '2880.hl.180.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536777
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.u1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1.a1', '60.u1.a1', '90.a1.a1', '90.h1.a1', '90.o1.a1'], 'contains': ['360.i1.a1', '360.m1.a1', '360.p1.a1', '360.ci1.a1', '360.cj1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8978, -1, 9418, -1, 9200, -1, 5825, -1], 'generators': [23, 122, 8023701, 3669143], 'label': '2880.hl.180.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536778
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.v1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.a1', '60.v1.a1', '90.b1.a1', '90.g1.a1', '90.o1.a1'], 'contains': ['360.i1.a1', '360.o1.a1', '360.q1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7103, -1, 7586, -1, 8223, -1, 6880, -1], 'generators': [23, 122, 8023693, 3669143], 'label': '2880.hl.180.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536779
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '180.w1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.a1', '60.w1.a1', '90.c1.a1', '90.g1.a1', '90.l1.a1'], 'contains': ['360.j1.a1', '360.k1.a1', '360.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7469, -1, 7986, -1, 8166, -1, 5720, -1], 'generators': [8023698, 9, 3669136, 16], 'label': '2880.hl.180.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536780
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.x1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1.a1', '60.x1.a1', '90.c1.a1', '90.e1.a1', '90.n1.a1'], 'contains': ['360.j1.a1', '360.n1.a1', '360.s1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7672, -1, 7488, -1, 7928, -1, 5651, -1], 'generators': [8023703, 23, 8025253, 3669143], 'label': '2880.hl.180.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536781
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': ['240.bq1.a1', '240.v1.a1', '240.bx1.a1', '240.x1.a1', '240.cd1.a1', '240.bz1.a1', '240.bt1.a1', '240.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.l1.a1', '6.u1.a1'], 'contains': ['24.c1.a1', '36.a1.a1', '48.bk1.a1', '60.bv1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5188, 2518, 5211, 3473, 4742, 7561, 2327, 2439], 'generators': [11, 23, 3669143, 8023692, 50803200, 7], 'label': '2880.hl.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.f1.a1', '6.b1.a1'], 'normal_contains': ['24.c1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536782
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '180.y1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1.a1', '60.y1.a1', '90.d1.a1', '90.h1.a1', '90.l1.a1'], 'contains': ['360.k1.a1', '360.l1.a1', '360.p1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9175, -1, 9371, -1, 8726, -1, 5484, -1], 'generators': [8023694, 9, 3669136, 16], 'label': '2880.hl.180.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536783
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.z1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1.a1', '60.z1.a1', '90.c1.a1', '90.h1.a1', '90.m1.a1'], 'contains': ['360.k1.a1', '360.m1.a1', '360.s1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7890, -1, 7377, -1, 7950, -1, 5599, -1], 'generators': [8025258, 9, 3669136, 16], 'label': '2880.hl.180.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536784
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.ba1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1.a1', '60.ba1.a1', '90.d1.a1', '90.g1.a1', '90.m1.a1'], 'contains': ['360.k1.a1', '360.q1.a1', '360.r1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8556, -1, 8774, -1, 8578, -1, 5697, -1], 'generators': [8025254, 9, 3669136, 16], 'label': '2880.hl.180.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536785
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bb1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1.a1', '60.bb1.a1', '90.d1.a1', '90.f1.a1', '90.n1.a1'], 'contains': ['360.l1.a1', '360.n1.a1', '360.r1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8524, -1, 8795, -1, 8553, -1, 5575, -1], 'generators': [23, 8025261, 3669143, 8023696], 'label': '2880.hl.180.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536786
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.bc1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1.a1', '60.bc1.a1', '90.c1.a1', '90.f1.a1', '90.o1.a1'], 'contains': ['360.m1.a1', '360.n1.a1', '360.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7246, -1, 8033, -1, 8249, -1, 5673, -1], 'generators': [23, 130, 8023693, 3669143], 'label': '2880.hl.180.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536787
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bd1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1.a1', '60.bd1.a1', '90.d1.a1', '90.e1.a1', '90.o1.a1'], 'contains': ['360.n1.a1', '360.p1.a1', '360.q1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9147, -1, 9391, -1, 9000, -1, 5509, -1], 'generators': [23, 130, 8023701, 3669143], 'label': '2880.hl.180.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536788
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.be1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1.a1', '60.be1.a1', '90.i1.a1'], 'contains': ['360.t1.a1', '360.u1.a1', '360.v1.a1', '360.x1.a1', '360.ba1.a1', '360.bd1.a1', '360.bg1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2915, -1, 2983, -1, 2790, -1, 3148, -1], 'generators': [127, 5, 3669143, 16], 'label': '2880.hl.180.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536789
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bf1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1.a1', '60.bf1.a1', '90.i1.a1'], 'contains': ['360.x1.a1', '360.y1.a1', '360.z1.a1', '360.bb1.a1', '360.bc1.a1', '360.be1.a1', '360.bf1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2413, -1, 1908, -1, 2428, -1, 3595, -1], 'generators': [127, 9, 3669143, 16], 'label': '2880.hl.180.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536790
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.bg1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1.a1', '60.bg1.a1', '60.bj1.a1', '90.i1.a1', '90.j1.a1', '90.k1.a1'], 'contains': ['360.a1.a1', '360.c1.a1', '360.h1.a1', '360.x1.a1', '360.bk1.a1', '360.bl1.a1', '360.bn1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4917, -1, 4806, -1, 4644, -1, 3488, -1], 'generators': [127, 23, 3669143, 7], 'label': '2880.hl.180.bg1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '180.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536791
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '180.bh1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1.a1', '60.bh1.a1', '60.bk1.a1', '90.i1.a1'], 'contains': ['360.b1.a1', '360.e1.a1', '360.t1.a1', '360.y1.a1', '360.bk1.a1', '360.bm1.a1', '360.bo1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1373, -1, 1250, -1, 747, -1, 2638, -1], 'generators': [127, 23, 5, 7], 'label': '2880.hl.180.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '180.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536792
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '480.a1.a1', 'complements': ['240.bq1.a1', '240.v1.a1', '240.bx1.a1', '240.x1.a1', '240.cd1.a1', '240.bz1.a1', '240.bt1.a1', '240.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1', '6.m1.a1', '6.v1.a1'], 'contains': ['24.c1.a1', '36.bn1.a1', '48.bm1.a1', '60.bx1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6373, 3972, 6443, 3947, 5370, 6215, 2159, 3786], 'generators': [11, 23, 8023697, 3669143, 50803200, 7], 'label': '2880.hl.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.h1.a1', '6.b1.a1'], 'normal_contains': ['24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
  • id: 183536793
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bi1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1.a1', '60.bi1.a1', '60.bl1.a1', '90.i1.a1'], 'contains': ['360.d1.a1', '360.f1.a1', '360.z1.a1', '360.ba1.a1', '360.bk1.a1', '360.bp1.a1', '360.bq1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1906, -1, 1387, -1, 864, -1, 2601, -1], 'generators': [3669138, 127, 23, 7], 'label': '2880.hl.180.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536794
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '180.bj1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1.a1', '60.bm1.a1', '60.bn1.a1', '90.i1.a1', '90.l1.a1', '90.m1.a1'], 'contains': ['360.g1.a1', '360.k1.a1', '360.v1.a1', '360.bf1.a1', '360.bl1.a1', '360.bm1.a1', '360.bp1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2814, -1, 1780, -1, 3585, -1, 2964, -1], 'generators': [23, 5, 3669143, 7], 'label': '2880.hl.180.bj1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536795
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bk1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1.a1', '60.bo1.a1', '60.bp1.a1', '60.bq1.a1', '90.i1.a1', '90.n1.a1', '90.o1.a1'], 'contains': ['360.i1.a1', '360.n1.a1', '360.be1.a1', '360.bg1.a1', '360.bl1.a1', '360.bo1.a1', '360.bq1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1819, -1, 2086, -1, 2158, -1, 2890, -1], 'generators': [23, 122, 3669143, 7], 'label': '2880.hl.180.bk1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536796
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '180.bl1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '30.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.br1.a1', '60.bv1.a1', '60.bz1.a1', '90.j1.a1', '90.l1.a1', '90.n1.a1'], 'contains': ['360.j1.a1', '360.l1.a1', '360.bl1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7915, -1, 8059, -1, 8395, -1, 4212, -1], 'generators': [23, 3669143, 8023696, 7], 'label': '2880.hl.180.bl1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '180.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536797
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.bm1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bm1.a1', '60.bs1.a1', '60.bw1.a1', '90.j1.a1', '90.m1.a1', '90.o1.a1'], 'contains': ['360.m1.a1', '360.q1.a1', '360.bl1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8793, -1, 8991, -1, 8966, -1, 4284, -1], 'generators': [8025256, 23, 3669143, 7], 'label': '2880.hl.180.bm1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '180.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536798
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '180.bn1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bn1.a1', '60.bt1.a1', '60.bx1.a1', '90.k1.a1', '90.l1.a1', '90.o1.a1'], 'contains': ['360.o1.a1', '360.p1.a1', '360.bl1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7037, -1, 7517, -1, 7976, -1, 4175, -1], 'generators': [23, 8023697, 3669143, 7], 'label': '2880.hl.180.bn1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536799
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bo1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bo1.a1', '60.bu1.a1', '60.by1.a1', '60.ca1.a1', '90.k1.a1', '90.m1.a1', '90.n1.a1'], 'contains': ['360.r1.a1', '360.s1.a1', '360.bl1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7404, -1, 7056, -1, 7815, -1, 4248, -1], 'generators': [23, 8025253, 3669143, 7], 'label': '2880.hl.180.bo1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536800
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bp1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bp1.a1', '60.cb1.a1', '60.cc1.a1', '90.i1.a1'], 'contains': ['360.u1.a1', '360.w1.a1', '360.bc1.a1', '360.bj1.a1', '360.bm1.a1', '360.bn1.a1', '360.bq1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1344, -1, 2232, -1, 1378, -1, 2442, -1], 'generators': [23, 5, 3669863, 7], 'label': '2880.hl.180.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536801
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '180.bq1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bq1.a1', '60.cd1.a1', '60.ce1.a1', '90.i1.a1'], 'contains': ['360.bb1.a1', '360.bd1.a1', '360.bh1.a1', '360.bi1.a1', '360.bn1.a1', '360.bo1.a1', '360.bp1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1305, -1, 1426, -1, 1415, -1, 2479, -1], 'generators': [3669138, 23, 3669863, 7], 'label': '2880.hl.180.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536802
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.br1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.br1.a1', '60.cf1.a1', '60.cg1.a1', '90.a1.a1'], 'contains': ['360.br1.a1', '360.bs1.a1', '360.bu1.a1', '360.by1.a1', '360.ca1.a1', '360.cg1.a1', '360.ci1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8251, -1, 8432, -1, 8353, -1, 6121, -1], 'generators': [5, 8023685, 3669120, 120], 'label': '2880.hl.180.br1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.br1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536803
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.n1.a1'], 'contains': ['24.h1.a1', '24.i1.a1', '24.k1.a1', '24.n1.a1', '24.p1.a1', '24.bb1.a1', '24.bi1.a1', '24.cf1.a1', '24.ci1.a1', '24.ck1.a1', '24.dc1.a1', '36.b1.a1', '60.a1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4481, -1, 4283, -1, 4442, -1, 7949, -1], 'generators': [3669960, 1456, 5, 120, 50803200, 16], 'label': '2880.hl.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.g1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536804
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.bs1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1.a1', '60.ch1.a1', '90.a1.a1'], 'contains': ['360.br1.a1', '360.bt1.a1', '360.bu1.a1', '360.bz1.a1', '360.cb1.a1', '360.ch1.a1', '360.cj1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9695, -1, 9763, -1, 9450, -1, 7408, -1], 'generators': [8023694, 5, 3669120, 120], 'label': '2880.hl.180.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536805
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.bt1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bt1.a1', '60.ci1.a1', '90.a1.a1'], 'contains': ['360.bx1.a1', '360.by1.a1', '360.cb1.a1', '360.cc1.a1', '360.cf1.a1', '360.cg1.a1', '360.cj1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8662, -1, 8841, -1, 9242, -1, 7293, -1], 'generators': [136, 5, 8023685, 3669120], 'label': '2880.hl.180.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536806
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '180.bu1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bu1.a1', '60.cj1.a1', '90.a1.a1'], 'contains': ['360.bx1.a1', '360.bz1.a1', '360.ca1.a1', '360.cd1.a1', '360.cf1.a1', '360.ch1.a1', '360.ci1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9352, -1, 9603, -1, 9284, -1, 7450, -1], 'generators': [136, 8023694, 5, 3669120], 'label': '2880.hl.180.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536807
    {'ambient': '2880.hl', 'aut_centralizer_order': 360, 'aut_label': '192.a1', 'aut_quo_index': 32, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '8.c1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.h1.a1', '96.j1.a1', '96.l1.a1', '96.m1.a1', '96.p1.a1', '96.r1.a1', '96.s1.a1'], 'contains': ['576.a1.a1', '960.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5096, 4028, 4881, 3613, 4583, 5009, 8384, 4991], 'generators': [1440, 50803200], 'label': '2880.hl.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1'], 'normal_contains': ['576.a1.a1', '960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '8.2', 'quotient_action_kernel': '24.12', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536808
    {'ambient': '2880.hl', 'aut_centralizer_order': 90, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '64.a1.a1', '96.e1.a1', '96.f1.a1', '96.i1.a1', '96.k1.a1', '96.n1.a1', '96.q1.a1', '96.t1.a1'], 'contains': ['576.a1.a1', '960.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2587, -1, 2152, -1, 1103, -1, 870, -1], 'generators': [11, 50803200], 'label': '2880.hl.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '192.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536809
    {'ambient': '2880.hl', 'aut_centralizer_order': 45, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 360, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1.a1', '64.a1.a1', '96.g1.a1', '96.o1.a1', '96.u1.a1'], 'contains': ['576.a1.a1', '960.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2649, -1, 2320, -1, 1216, -1, 1199, -1], 'generators': [1460, 50803200], 'label': '2880.hl.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '192.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 183536810
    {'ambient': '2880.hl', 'aut_centralizer_order': 240, 'aut_label': '240.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '12.c1.a1', 'complements': ['12.cf1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.bn1.a1', '120.bq1.a1', '120.bs1.a1', '120.bt1.a1', '120.bw1.a1', '120.by1.a1'], 'contains': ['480.b1.a1', '720.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1566, 5762, 1605, 5753, 2059, 3553, 2411, 6432], 'generators': [23, 1456, 7], 'label': '2880.hl.240.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1'], 'normal_contains': ['720.a1.a1', '960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '12.4', 'quotient_action_kernel': '20.3', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536811
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '240.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '24.g1.a1', 'complements': ['12.ci1.a1', '12.cj1.a1', '12.ch1.a1', '12.cg1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.a1.a1', '120.b1.a1', '120.bm1.a1', '120.bo1.a1', '120.br1.a1', '120.bu1.a1', '120.bx1.a1', '120.bz1.a1'], 'contains': ['720.a1.a1', '960.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [243, 6691, 242, 6603, 164, 3024, 783, 6960], 'generators': [11, 23, 7], 'label': '2880.hl.240.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.b1.a1', 'normal_contained_in': ['48.b1.a1', '80.a1.a1', '120.b1.a1'], 'normal_contains': ['720.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.2', 'quotient_action_kernel': '60.6', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536812
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '120.a1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.f1.a1', '120.g1.a1', '120.h1.a1'], 'contains': ['480.a1.a1', '480.b1.a1', '480.i1.a1', '720.b1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3709, -1, 3629, -1, 3577, -1, 4007, -1], 'generators': [127, 1447, 7], 'label': '2880.hl.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '240.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536813
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '120.c1.a1', '120.i1.a1', '120.j1.a1', '120.k1.a1', '120.l1.a1', '120.m1.a1', '120.n1.a1', '120.o1.a1', '120.p1.a1', '120.q1.a1', '120.r1.a1', '120.s1.a1', '120.t1.a1', '120.u1.a1', '120.bn1.a1'], 'contains': ['480.b1.a1', '480.d1.a1', '480.l1.a1', '720.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6498, -1, 6598, -1, 6943, -1, 6602, -1], 'generators': [3669967, 1447, 7], 'label': '2880.hl.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536814
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '120.36', 'aut_weyl_index': 24, 'centralizer': '360.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.q1.a1', '24.t1.a1', '24.cg1.a1', '24.cr1.a1', '24.cs1.a1', '36.c1.a1', '60.b1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8432, -1, 8458, -1, 7159, -1, 8664, -1], 'generators': [127, 8025127, 3669967, 1447, 50803200, 7], 'label': '2880.hl.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.h1.a1', 'projective_image': '2880.hl', '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': '120.36'}
  • id: 183536815
    {'ambient': '2880.hl', 'aut_centralizer_order': 240, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '12.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '120.d1.a1', '120.i1.a1', '120.v1.a1', '120.w1.a1', '120.x1.a1', '120.y1.a1', '120.bq1.a1'], 'contains': ['480.b1.a1', '480.g1.a1', '720.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3779, -1, 3930, -1, 3549, -1, 3683, -1], 'generators': [1456, 5, 16], 'label': '2880.hl.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '240.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536816
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '120.a1.a1', '120.j1.a1', '120.v1.a1', '120.z1.a1', '120.ba1.a1', '120.bb1.a1', '120.bc1.a1'], 'contains': ['480.b1.a1', '480.i1.a1', '720.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3849, -1, 3782, -1, 3615, -1, 3832, -1], 'generators': [136, 1447, 7], 'label': '2880.hl.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '240.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536817
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '120.c1.a1', '120.w1.a1', '120.z1.a1', '120.bd1.a1', '120.be1.a1', '120.bf1.a1', '120.bs1.a1'], 'contains': ['480.b1.a1', '480.k1.a1', '480.r1.a1', '720.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3594, -1, 3703, -1, 3596, -1, 4063, -1], 'generators': [1447, 3669840, 7], 'label': '2880.hl.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536818
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '120.e1.a1', '120.x1.a1', '120.z1.a1', '120.bg1.a1', '120.bh1.a1', '120.bi1.a1', '120.bn1.a1'], 'contains': ['480.b1.a1', '480.l1.a1', '720.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4535, -1, 4585, -1, 3730, -1, 3428, -1], 'generators': [1447, 3669976, 7], 'label': '2880.hl.240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536819
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '120.d1.a1', '120.k1.a1', '120.ba1.a1', '120.bd1.a1', '120.bg1.a1', '120.bj1.a1', '120.bt1.a1'], 'contains': ['480.b1.a1', '480.m1.a1', '720.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3461, -1, 3434, -1, 3439, -1, 3939, -1], 'generators': [23, 122, 1463], 'label': '2880.hl.240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '240.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536820
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '120.f1.a1', '120.i1.a1', '120.bb1.a1', '120.bd1.a1', '120.bh1.a1', '120.bk1.a1', '120.bw1.a1'], 'contains': ['480.b1.a1', '480.p1.a1', '720.i1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3347, -1, 3203, -1, 3489, -1, 4035, -1], 'generators': [1456, 3669965, 16], 'label': '2880.hl.240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536821
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '120.e1.a1', '120.j1.a1', '120.y1.a1', '120.bj1.a1', '120.bk1.a1', '120.bl1.a1', '120.bs1.a1'], 'contains': ['480.b1.a1', '480.r1.a1', '720.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3817, -1, 3741, -1, 3635, -1, 3655, -1], 'generators': [1447, 3669863, 7], 'label': '2880.hl.240.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536822
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '120.f1.a1', '120.k1.a1', '120.w1.a1', '120.bc1.a1', '120.bi1.a1', '120.bl1.a1', '120.by1.a1'], 'contains': ['480.b1.a1', '480.s1.a1', '720.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3306, -1, 3551, -1, 3352, -1, 3870, -1], 'generators': [23, 1463, 3669842], 'label': '2880.hl.240.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536823
    {'ambient': '2880.hl', 'aut_centralizer_order': 240, 'aut_label': '240.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '12.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '120.g1.a1', '120.m1.a1', '120.ba1.a1', '120.be1.a1', '120.bh1.a1', '120.bl1.a1', '120.bq1.a1'], 'contains': ['480.b1.a1', '720.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1754, -1, 1841, -1, 2722, -1, 3754, -1], 'generators': [1456, 9, 16], 'label': '2880.hl.240.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '240.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536824
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '240.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '120.g1.a1', '120.p1.a1', '120.v1.a1', '120.bf1.a1', '120.bi1.a1', '120.bk1.a1', '120.bt1.a1'], 'contains': ['480.b1.a1', '720.m1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2046, -1, 2031, -1, 2746, -1, 3519, -1], 'generators': [23, 130, 1463], 'label': '2880.hl.240.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '240.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536825
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.n1.a1'], 'contains': ['24.h1.a1', '24.l1.a1', '24.m1.a1', '24.r1.a1', '24.u1.a1', '24.bj1.a1', '24.bk1.a1', '36.d1.a1', '60.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1851, -1, 1719, -1, 2736, -1, 4747, -1], 'generators': [3669960, 1456, 9, 120, 50803200, 16], 'label': '2880.hl.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536826
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '240.o1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '120.h1.a1', '120.m1.a1', '120.x1.a1', '120.bc1.a1', '120.bf1.a1', '120.bj1.a1', '120.bw1.a1'], 'contains': ['480.b1.a1', '720.n1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2294, -1, 2051, -1, 2908, -1, 3317, -1], 'generators': [1456, 3669969, 16], 'label': '2880.hl.240.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536827
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.p1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '12.4', 'aut_weyl_index': 240, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '120.h1.a1', '120.p1.a1', '120.y1.a1', '120.bb1.a1', '120.be1.a1', '120.bg1.a1', '120.by1.a1'], 'contains': ['480.b1.a1', '720.o1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2129, -1, 2304, -1, 2771, -1, 3458, -1], 'generators': [23, 1463, 3669850], 'label': '2880.hl.240.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 183536828
    {'ambient': '2880.hl', 'aut_centralizer_order': 60, 'aut_label': '240.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 120, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1.a1', '80.a1.a1', '120.bp1.a1', '120.bv1.a1', '120.ca1.a1'], 'contains': ['720.a1.a1', '960.c1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [259, -1, 259, -1, 327, -1, 1097, -1], 'generators': [23, 1460, 7], 'label': '2880.hl.240.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '240.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 183536829
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '240.r1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '120.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.a1', '60.bg1.a1', '80.b1.a1', '120.cb1.a1', '120.cc1.a1', '120.cd1.a1'], 'contains': ['480.c1.a1', '480.e1.a1', '480.j1.a1', '720.p1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1714, -1, 1634, -1, 1082, -1, 1550, -1], 'generators': [124, 3669120, 3], 'label': '2880.hl.240.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '240.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536830
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '240.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.a1', '60.bh1.a1', '80.c1.a1', '120.cb1.a1'], 'contains': ['480.c1.a1', '480.h1.a1', '480.n1.a1', '720.q1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2478, -1, 2465, -1, 1375, -1, 967, -1], 'generators': [124, 5, 3], 'label': '2880.hl.240.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '240.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.s1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536831
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '240.t1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '60.bi1.a1', '80.d1.a1', '120.cb1.a1'], 'contains': ['480.c1.a1', '480.q1.a1', '480.t1.a1', '720.s1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1882, -1, 1312, -1, 809, -1, 903, -1], 'generators': [3669125, 124, 3], 'label': '2880.hl.240.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '240.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536832
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '240.u1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '30.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '80.b1.a1', '120.c1.a1', '120.ce1.a1', '120.cf1.a1', '120.cg1.a1', '120.ch1.a1'], 'contains': ['480.a1.a1', '480.d1.a1', '480.k1.a1', '720.p1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4244, -1, 4467, -1, 5282, -1, 7147, -1], 'generators': [1440, 3669960, 120], 'label': '2880.hl.240.u1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '240.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536833
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '240.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1.a1', '80.c1.a1', '120.d1.a1', '120.ce1.a1', '120.ci1.a1'], 'contains': ['480.a1.a1', '480.g1.a1', '480.m1.a1', '720.q1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4276, -1, 4246, -1, 4438, -1, 7569, -1], 'generators': [1440, 5, 120], 'label': '2880.hl.240.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '240.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.v1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536834
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '240.w1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1.a1', '120.c1.a1', '120.e1.a1', '120.ci1.a1', '120.cj1.a1'], 'contains': ['480.a1.a1', '480.l1.a1', '480.r1.a1', '720.r1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5884, -1, 5886, -1, 5778, -1, 7907, -1], 'generators': [1440, 3669967, 120], 'label': '2880.hl.240.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536835
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.x1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1.a1', '80.d1.a1', '120.f1.a1', '120.ce1.a1', '120.ci1.a1'], 'contains': ['480.a1.a1', '480.p1.a1', '480.s1.a1', '720.s1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4402, -1, 4554, -1, 4357, -1, 7644, -1], 'generators': [1440, 3669974, 120], 'label': '2880.hl.240.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536836
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.h1.a1', '24.s1.a1', '24.x1.a1', '24.cg1.a1', '24.ct1.a1', '36.e1.a1', '60.d1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9438, -1, 9389, -1, 8052, -1, 8308, -1], 'generators': [127, 3669967, 8025136, 1447, 50803200, 7], 'label': '2880.hl.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536837
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '240.y1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1.a1', '80.e1.a1', '120.i1.a1', '120.ce1.a1', '120.ck1.a1', '120.cl1.a1', '120.cm1.a1', '120.cn1.a1', '120.co1.a1'], 'contains': ['480.d1.a1', '480.g1.a1', '480.p1.a1', '720.t1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5730, -1, 5855, -1, 6214, -1, 7596, -1], 'generators': [1440, 3669960, 5], 'label': '2880.hl.240.y1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536838
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '240.z1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1.a1', '60.bn1.a1', '80.e1.a1', '120.cb1.a1', '120.cp1.a1', '120.cq1.a1'], 'contains': ['480.e1.a1', '480.h1.a1', '480.q1.a1', '720.t1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3050, -1, 3411, -1, 3094, -1, 1304, -1], 'generators': [11, 5, 3669120], 'label': '2880.hl.240.z1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '240.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536839
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '240.ba1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '120.c1.a1', '120.j1.a1', '120.ck1.a1', '120.cr1.a1', '120.cs1.a1', '120.ct1.a1', '120.cu1.a1'], 'contains': ['480.d1.a1', '480.i1.a1', '480.r1.a1', '720.u1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6585, -1, 6748, -1, 6971, -1, 7663, -1], 'generators': [136, 1440, 3669960], 'label': '2880.hl.240.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536840
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.bb1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1.a1', '80.f1.a1', '120.k1.a1', '120.ce1.a1', '120.ck1.a1', '120.cv1.a1', '120.cw1.a1', '120.cx1.a1', '120.cy1.a1'], 'contains': ['480.d1.a1', '480.m1.a1', '480.s1.a1', '720.v1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4935, -1, 5530, -1, 5301, -1, 7530, -1], 'generators': [1440, 3669960, 122], 'label': '2880.hl.240.bb1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536841
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '240.bc1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1.a1', '60.bp1.a1', '80.f1.a1', '120.cb1.a1', '120.cz1.a1', '120.da1.a1'], 'contains': ['480.e1.a1', '480.n1.a1', '480.t1.a1', '720.v1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2629, -1, 2781, -1, 3075, -1, 1375, -1], 'generators': [122, 3669120, 12], 'label': '2880.hl.240.bc1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '240.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536842
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '240.bd1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1.a1', '60.bq1.a1', '80.f1.a1', '120.db1.a1'], 'contains': ['480.f1.a1', '480.o1.a1', '480.u1.a1', '720.v1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [3035, -1, 3387, -1, 3312, -1, 1460, -1], 'generators': [122, 1443, 3669964], 'label': '2880.hl.240.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.db1.a1', 'old_label': '240.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536843
    {'ambient': '2880.hl', 'aut_centralizer_order': 288, 'aut_label': '240.be1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '10.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '80.g1.a1', '120.l1.a1', '120.cf1.a1', '120.cl1.a1', '120.cr1.a1', '120.cv1.a1'], 'contains': ['480.d1.a1', '720.w1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7941, -1, 7981, -1, 8287, -1, 7066, -1], 'generators': [8025120, 1440, 3669960], 'label': '2880.hl.240.be1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '240.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536844
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '240.bf1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1.a1', '120.l1.a1', '120.n1.a1', '120.cg1.a1', '120.cm1.a1', '120.cs1.a1', '120.ct1.a1', '120.cw1.a1'], 'contains': ['480.d1.a1', '720.x1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9081, -1, 9275, -1, 9109, -1, 7684, -1], 'generators': [1440, 3669960, 8025136], 'label': '2880.hl.240.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536845
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '240.bg1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '30.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '80.h1.a1', '120.o1.a1', '120.cf1.a1', '120.cn1.a1', '120.cs1.a1', '120.cx1.a1'], 'contains': ['480.d1.a1', '720.y1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8194, -1, 8405, -1, 8445, -1, 7041, -1], 'generators': [1440, 3669960, 8025240], 'label': '2880.hl.240.bg1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '240.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536846
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '240.bh1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.a1', '80.i1.a1', '120.r1.a1', '120.ch1.a1', '120.cl1.a1', '120.cm1.a1', '120.cu1.a1', '120.cx1.a1', '120.cy1.a1'], 'contains': ['480.d1.a1', '720.z1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8750, -1, 8943, -1, 8542, -1, 7089, -1], 'generators': [1440, 3669960, 8025126], 'label': '2880.hl.240.bh1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536847
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.o1.a1'], 'contains': ['24.h1.a1', '24.v1.a1', '24.z1.a1', '24.cj1.a1', '24.dd1.a1', '36.f1.a1', '60.e1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6733, -1, 6595, -1, 6077, -1, 8573, -1], 'generators': [127, 3669967, 1447, 8025137, 50803200, 7], 'label': '2880.hl.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536848
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '240.bi1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1.a1', '120.o1.a1', '120.s1.a1', '120.cg1.a1', '120.co1.a1', '120.cr1.a1', '120.ct1.a1', '120.cy1.a1'], 'contains': ['480.d1.a1', '720.ba1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8925, -1, 9248, -1, 9212, -1, 7471, -1], 'generators': [8025256, 1440, 3669960], 'label': '2880.hl.240.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536849
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.bj1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1.a1', '80.j1.a1', '120.t1.a1', '120.ch1.a1', '120.cn1.a1', '120.co1.a1', '120.cu1.a1', '120.cv1.a1', '120.cw1.a1'], 'contains': ['480.d1.a1', '720.bb1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8597, -1, 8724, -1, 8420, -1, 7169, -1], 'generators': [1440, 3669960, 8025261], 'label': '2880.hl.240.bj1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536850
    {'ambient': '2880.hl', 'aut_centralizer_order': 72, 'aut_label': '240.bk1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '40.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1.a1', '60.bv1.a1', '80.g1.a1', '120.cc1.a1', '120.cp1.a1', '120.cz1.a1'], 'contains': ['480.e1.a1', '720.w1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5623, -1, 5746, -1, 5500, -1, 1840, -1], 'generators': [3669120, 8023692, 12], 'label': '2880.hl.240.bk1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '240.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536851
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '240.bl1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '120.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bl1.a1', '60.bw1.a1', '80.h1.a1', '120.cc1.a1', '120.cq1.a1', '120.da1.a1'], 'contains': ['480.e1.a1', '720.y1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5778, -1, 6100, -1, 5573, -1, 1662, -1], 'generators': [8025255, 3669120, 20], 'label': '2880.hl.240.bl1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '240.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536852
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '240.bm1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.a1', '60.bx1.a1', '80.i1.a1', '120.cd1.a1', '120.cp1.a1', '120.da1.a1'], 'contains': ['480.e1.a1', '720.z1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6359, -1, 6453, -1, 5597, -1, 1591, -1], 'generators': [11, 3669120, 8023686], 'label': '2880.hl.240.bm1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '240.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536853
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '240.bn1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '60.by1.a1', '80.j1.a1', '120.cd1.a1', '120.cq1.a1', '120.cz1.a1'], 'contains': ['480.e1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6258, -1, 6334, -1, 5549, -1, 1780, -1], 'generators': [11, 3669120, 8025261], 'label': '2880.hl.240.bn1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '240.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536854
    {'ambient': '2880.hl', 'aut_centralizer_order': 36, 'aut_label': '240.bo1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '80.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '60.bz1.a1', '80.g1.a1', '120.db1.a1'], 'contains': ['480.f1.a1', '720.w1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [5658, -1, 5766, -1, 6359, -1, 1929, -1], 'generators': [8025132, 1452, 3669968], 'label': '2880.hl.240.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.m1.a1', 'old_label': '240.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536855
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '240.bp1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '60.ca1.a1', '80.j1.a1', '120.db1.a1'], 'contains': ['480.f1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [6317, -1, 6399, -1, 6401, -1, 1963, -1], 'generators': [3669979, 1451, 8025261], 'label': '2880.hl.240.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.db1.a1', 'old_label': '240.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536856
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '240.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1.a1', '120.d1.a1', '120.ck1.a1', '120.dc1.a1'], 'contains': ['480.g1.a1', '480.i1.a1', '480.m1.a1', '720.bc1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5329, -1, 5456, -1, 5220, -1, 7829, -1], 'generators': [136, 1440, 5], 'label': '2880.hl.240.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '240.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536857
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.br1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a1', '80.k1.a1', '120.w1.a1', '120.ce1.a1', '120.dc1.a1'], 'contains': ['480.g1.a1', '480.k1.a1', '480.s1.a1', '720.bd1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4376, -1, 5102, -1, 4400, -1, 7549, -1], 'generators': [1440, 5, 3669840], 'label': '2880.hl.240.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.br1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536858
    {'ambient': '2880.hl', 'aut_centralizer_order': 1, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2880.hl', 'aut_weyl_index': 1, 'centralizer': '2880.a1.a1', 'complements': ['1440.d1.a1', '1440.i1.a1', '1440.b1.a1', '1440.e1.a1', '1440.f1.a1', '1440.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.g1.a1', '4.h1.a1', '6.t1.a1', '6.v1.a1', '8.n1.a1', '10.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6081, 3499, 6148, 2775, 5353, 6598, 2166, 3402], 'generators': [11, 23, 3669967, 122, 1456, 8025137, 50803200, 7], 'label': '2880.hl.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.g1.a1', '4.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2880.hl'}
  • id: 183536859
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.o1.a1'], 'contains': ['24.h1.a1', '24.w1.a1', '24.y1.a1', '24.ch1.a1', '24.cu1.a1', '36.g1.a1', '60.f1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8806, -1, 8628, -1, 6482, -1, 8084, -1], 'generators': [127, 3669967, 1447, 8025126, 50803200, 7], 'label': '2880.hl.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '2880.hl', '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': '240.195'}
  • id: 183536860
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '240.bs1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '120.i1.a1', '120.ci1.a1', '120.dc1.a1'], 'contains': ['480.g1.a1', '480.l1.a1', '480.p1.a1', '720.be1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5392, -1, 5669, -1, 5675, -1, 8019, -1], 'generators': [1440, 5, 3669976], 'label': '2880.hl.240.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536861
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.bt1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '120.w1.a1', '120.ci1.a1', '120.ck1.a1'], 'contains': ['480.g1.a1', '480.r1.a1', '480.s1.a1', '720.bf1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5314, -1, 5424, -1, 5239, -1, 7868, -1], 'generators': [1440, 5, 3669856], 'label': '2880.hl.240.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536862
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '240.bu1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '60.cc1.a1', '80.k1.a1', '120.cb1.a1'], 'contains': ['480.h1.a1', '480.j1.a1', '480.t1.a1', '720.bd1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2096, -1, 2384, -1, 1235, -1, 717, -1], 'generators': [5, 3669844, 3], 'label': '2880.hl.240.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '240.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536863
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '240.bv1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1.a1', '120.c1.a1', '120.z1.a1', '120.dc1.a1', '120.dd1.a1'], 'contains': ['480.i1.a1', '480.k1.a1', '480.l1.a1', '720.bg1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5899, -1, 5901, -1, 5759, -1, 7810, -1], 'generators': [127, 1440, 3669967], 'label': '2880.hl.240.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '240.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536864
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.bw1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '120.e1.a1', '120.j1.a1', '120.z1.a1'], 'contains': ['480.i1.a1', '480.l1.a1', '480.r1.a1', '720.bh1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5860, -1, 5807, -1, 5703, -1, 6107, -1], 'generators': [1440, 143, 3669967], 'label': '2880.hl.240.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.m1.a1', 'old_label': '240.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536865
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.bx1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '120.f1.a1', '120.ck1.a1', '120.dc1.a1'], 'contains': ['480.i1.a1', '480.p1.a1', '480.s1.a1', '720.bi1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5290, -1, 5409, -1, 5097, -1, 7849, -1], 'generators': [136, 1440, 3669974], 'label': '2880.hl.240.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536866
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '240.by1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1.a1', '60.cd1.a1', '80.l1.a1', '120.cb1.a1'], 'contains': ['480.j1.a1', '480.n1.a1', '480.q1.a1', '720.bj1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1842, -1, 1271, -1, 1216, -1, 883, -1], 'generators': [3669125, 3669844, 3], 'label': '2880.hl.240.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '240.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.by1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536867
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.bz1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1.a1', '80.l1.a1', '120.bd1.a1', '120.ce1.a1', '120.dc1.a1'], 'contains': ['480.k1.a1', '480.m1.a1', '480.p1.a1', '720.bj1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4133, -1, 4360, -1, 4419, -1, 7624, -1], 'generators': [1440, 3669840, 3669974], 'label': '2880.hl.240.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536868
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.ca1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1.a1', '120.k1.a1', '120.ci1.a1', '120.dc1.a1'], 'contains': ['480.l1.a1', '480.m1.a1', '480.s1.a1', '720.bk1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4662, -1, 5253, -1, 5078, -1, 7992, -1], 'generators': [1440, 122, 3669983], 'label': '2880.hl.240.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536869
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '240.cb1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1.a1', '120.q1.a1', '120.cj1.a1', '120.dd1.a1'], 'contains': ['480.l1.a1', '720.bl1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6527, -1, 6801, -1, 7211, -1, 8158, -1], 'generators': [1440, 3669967, 8025137], 'label': '2880.hl.240.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536870
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1'], 'contains': ['24.i1.a1', '24.j1.a1', '24.m1.a1', '24.bc1.a1', '24.bd1.a1', '24.bl1.a1', '24.bo1.a1', '36.h1.a1', '60.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3505, -1, 3475, -1, 3378, -1, 3664, -1], 'generators': [3669967, 1456, 5, 120, 50803200, 16], 'label': '2880.hl.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '2880.hl', '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': '480.1197'}
  • id: 183536871
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.cc1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1.a1', '120.u1.a1', '120.cj1.a1', '120.dd1.a1'], 'contains': ['480.l1.a1', '720.bm1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6678, -1, 6656, -1, 7074, -1, 8219, -1], 'generators': [1440, 3669983, 8025253], 'label': '2880.hl.240.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '240.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536872
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '240.cd1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1.a1', '120.bd1.a1', '120.ci1.a1', '120.ck1.a1'], 'contains': ['480.m1.a1', '480.p1.a1', '480.r1.a1', '720.bn1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5140, -1, 4805, -1, 5116, -1, 7887, -1], 'generators': [1440, 3669856, 3669974], 'label': '2880.hl.240.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '240.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536873
    {'ambient': '2880.hl', 'aut_centralizer_order': 144, 'aut_label': '288.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.f1.a1', '96.g1.a1', '144.b1.a1', '144.d1.a1', '144.q1.a1', '144.u1.a1', '144.v1.a1', '144.w1.a1', '144.x1.a1', '144.y1.a1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1'], 'contains': ['576.a1.a1', '1440.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7181, 2564, 6789, 2720, 6327, 6837, 7868, 3257], 'generators': [3669120, 50803200], 'label': '2880.hl.288.a1.a1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.a1.a1', '96.b1.a1', '144.b1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '2880.hl', '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': '20.3'}
  • id: 183536874
    {'ambient': '2880.hl', 'aut_centralizer_order': 240, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '12.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '144.a1.a1', '144.c1.a1', '144.d1.a1', '144.e1.a1', '144.f1.a1', '144.g1.a1', '144.h1.a1', '144.i1.a1', '144.j1.a1', '144.k1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1', '144.o1.a1', '144.p1.a1'], 'contains': ['576.a1.a1', '1440.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3196, -1, 2852, -1, 3127, -1, 4653, -1], 'generators': [50803200, 7], 'label': '2880.hl.288.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536875
    {'ambient': '2880.hl', 'aut_centralizer_order': 240, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '12.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.e1.a1', '144.c1.a1', '144.q1.a1', '144.r1.a1', '144.s1.a1', '144.t1.a1'], 'contains': ['576.a1.a1', '1440.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4055, -1, 3343, -1, 4290, -1, 7950, -1], 'generators': [120, 50803200], 'label': '2880.hl.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '288.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536876
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.i1.a1', '144.e1.a1', '144.r1.a1', '144.u1.a1', '144.bc1.a1', '144.bd1.a1', '144.be1.a1', '144.bf1.a1'], 'contains': ['576.a1.a1', '1440.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5190, -1, 4953, -1, 4521, -1, 8408, -1], 'generators': [5, 50803200], 'label': '2880.hl.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '288.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536877
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '36.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1', '144.c1.a1', '144.f1.a1', '144.v1.a1', '144.bc1.a1', '144.bg1.a1', '144.bh1.a1', '144.bi1.a1'], 'contains': ['576.a1.a1', '1440.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5473, -1, 5283, -1, 4828, -1, 8115, -1], 'generators': [127, 50803200], 'label': '2880.hl.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536878
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.k1.a1', '144.g1.a1', '144.q1.a1', '144.bd1.a1', '144.bg1.a1', '144.bj1.a1'], 'contains': ['576.a1.a1', '1440.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3976, -1, 4096, -1, 4311, -1, 7929, -1], 'generators': [3669840, 50803200], 'label': '2880.hl.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '288.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536879
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '60.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.l1.a1', '144.d1.a1', '144.h1.a1', '144.s1.a1', '144.be1.a1', '144.bg1.a1', '144.bh1.a1', '144.bk1.a1', '144.bl1.a1', '144.bm1.a1'], 'contains': ['576.a1.a1', '1440.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5666, -1, 5546, -1, 5439, -1, 8591, -1], 'generators': [3669143, 50803200], 'label': '2880.hl.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536880
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.m1.a1', '96.n1.a1', '96.o1.a1', '144.i1.a1', '144.r1.a1', '144.w1.a1', '144.bc1.a1', '144.bj1.a1', '144.bk1.a1', '144.bn1.a1'], 'contains': ['576.a1.a1', '1440.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4312, -1, 4114, -1, 4352, -1, 8226, -1], 'generators': [122, 50803200], 'label': '2880.hl.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '288.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536881
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1'], 'contains': ['24.j1.a1', '24.k1.a1', '24.l1.a1', '24.bm1.a1', '24.bn1.a1', '24.bp1.a1', '24.bq1.a1', '36.i1.a1', '60.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2562, -1, 3011, -1, 3004, -1, 4082, -1], 'generators': [3669967, 1456, 9, 120, 50803200, 16], 'label': '2880.hl.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536882
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '96.q1.a1', '144.j1.a1', '144.t1.a1', '144.u1.a1', '144.be1.a1', '144.bi1.a1', '144.bj1.a1', '144.bn1.a1'], 'contains': ['576.a1.a1', '1440.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4976, -1, 4507, -1, 4499, -1, 8468, -1], 'generators': [3669125, 50803200], 'label': '2880.hl.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '288.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536883
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '180.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1.a1', '144.g1.a1', '144.k1.a1', '144.s1.a1', '144.v1.a1', '144.bf1.a1', '144.bh1.a1', '144.bn1.a1'], 'contains': ['576.a1.a1', '1440.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5423, -1, 5258, -1, 4850, -1, 8248, -1], 'generators': [3669863, 50803200], 'label': '2880.hl.288.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536884
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 144, 'centralizer': '360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.s1.a1', '96.t1.a1', '96.u1.a1', '144.l1.a1', '144.t1.a1', '144.w1.a1', '144.bd1.a1', '144.bf1.a1', '144.bi1.a1', '144.bk1.a1'], 'contains': ['576.a1.a1', '1440.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4757, -1, 4690, -1, 4330, -1, 8205, -1], 'generators': [3669842, 50803200], 'label': '2880.hl.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '288.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 183536885
    {'ambient': '2880.hl', 'aut_centralizer_order': 180, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '80.a1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1', '160.d1.a1', '160.e1.a1', '160.f1.a1', '160.g1.a1'], 'contains': ['960.a1.a1', '960.b1.a1', '960.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [870, -1, 988, -1, 1194, -1, 533, -1], 'generators': [11, 1440], 'label': '2880.hl.320.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '320.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536886
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '120.c1.a1', '180.a1.a1', '180.b1.a1', '180.c1.a1', '180.d1.a1', '180.e1.a1', '180.f1.a1', '180.bg1.a1'], 'contains': ['720.b1.a1', '720.c1.a1', '720.f1.a1', '720.p1.a1', '720.r1.a1', '720.u1.a1', '720.bg1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6393, -1, 6303, -1, 6507, -1, 6476, -1], 'generators': [127, 3669120, 7], 'label': '2880.hl.360.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536887
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '120.d1.a1', '180.a1.a1', '180.g1.a1', '180.bh1.a1'], 'contains': ['720.b1.a1', '720.d1.a1', '720.h1.a1', '720.q1.a1', '720.bc1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3417, -1, 3446, -1, 3460, -1, 3964, -1], 'generators': [5, 120, 16], 'label': '2880.hl.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '360.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536888
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '120.e1.a1', '180.g1.a1', '180.h1.a1', '180.bg1.a1'], 'contains': ['720.b1.a1', '720.g1.a1', '720.j1.a1', '720.r1.a1', '720.bh1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4849, -1, 4687, -1, 3701, -1, 3732, -1], 'generators': [127, 3669143, 7], 'label': '2880.hl.360.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536889
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.f1.a1', '180.a1.a1', '180.h1.a1', '180.bi1.a1'], 'contains': ['720.b1.a1', '720.i1.a1', '720.k1.a1', '720.s1.a1', '720.bi1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3322, -1, 2935, -1, 3178, -1, 4274, -1], 'generators': [3669134, 120, 16], 'label': '2880.hl.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536890
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.g1.a1', '180.c1.a1', '180.h1.a1', '180.bh1.a1'], 'contains': ['720.b1.a1', '720.l1.a1', '720.m1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1356, -1, 1296, -1, 1118, -1, 3608, -1], 'generators': [9, 120, 16], 'label': '2880.hl.360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '360.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536891
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '120.h1.a1', '180.c1.a1', '180.g1.a1', '180.bi1.a1'], 'contains': ['720.b1.a1', '720.n1.a1', '720.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1939, -1, 1652, -1, 2244, -1, 3287, -1], 'generators': [3669138, 120, 16], 'label': '2880.hl.360.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536892
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.h1.a1', '6.n1.a1'], 'contains': ['24.n1.a1', '24.o1.a1', '24.u1.a1', '24.ba1.a1', '24.bd1.a1', '24.bg1.a1', '24.bp1.a1', '36.j1.a1', '60.i1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3747, -1, 3760, -1, 3571, -1, 4906, -1], 'generators': [127, 3669960, 1456, 5, 50803200, 16], 'label': '2880.hl.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536893
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '120.i1.a1', '180.a1.a1', '180.i1.a1', '180.j1.a1', '180.k1.a1', '180.l1.a1', '180.m1.a1', '180.bj1.a1'], 'contains': ['720.c1.a1', '720.d1.a1', '720.i1.a1', '720.t1.a1', '720.be1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5680, -1, 5783, -1, 5992, -1, 6449, -1], 'generators': [5, 3669136, 16], 'label': '2880.hl.360.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536894
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '120.j1.a1', '180.i1.a1', '180.n1.a1', '180.o1.a1', '180.p1.a1', '180.q1.a1', '180.r1.a1', '180.bg1.a1'], 'contains': ['720.c1.a1', '720.e1.a1', '720.j1.a1', '720.u1.a1', '720.bh1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6411, -1, 6502, -1, 6485, -1, 5686, -1], 'generators': [136, 3669120, 7], 'label': '2880.hl.360.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536895
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '120.k1.a1', '180.a1.a1', '180.n1.a1', '180.s1.a1', '180.t1.a1', '180.u1.a1', '180.v1.a1', '180.bk1.a1'], 'contains': ['720.c1.a1', '720.h1.a1', '720.k1.a1', '720.v1.a1', '720.bk1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4602, -1, 5053, -1, 4991, -1, 6390, -1], 'generators': [23, 122, 3669143], 'label': '2880.hl.360.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536896
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '120.l1.a1', '180.b1.a1', '180.j1.a1', '180.o1.a1', '180.s1.a1', '180.w1.a1', '180.x1.a1', '180.bl1.a1'], 'contains': ['720.c1.a1', '720.w1.a1', '720.x1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8279, -1, 8267, -1, 8582, -1, 6420, -1], 'generators': [3669120, 8023687, 7], 'label': '2880.hl.360.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536897
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '120.m1.a1', '180.c1.a1', '180.n1.a1', '180.w1.a1', '180.y1.a1', '180.z1.a1', '180.ba1.a1', '180.bj1.a1'], 'contains': ['720.c1.a1', '720.l1.a1', '720.n1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3017, -1, 2635, -1, 4599, -1, 5424, -1], 'generators': [9, 3669136, 16], 'label': '2880.hl.360.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536898
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '120.n1.a1', '180.d1.a1', '180.k1.a1', '180.p1.a1', '180.t1.a1', '180.y1.a1', '180.bb1.a1', '180.bl1.a1'], 'contains': ['720.c1.a1', '720.x1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8940, -1, 9234, -1, 8693, -1, 6639, -1], 'generators': [3669120, 8023696, 7], 'label': '2880.hl.360.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536899
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1.a1', '120.o1.a1', '180.b1.a1', '180.l1.a1', '180.p1.a1', '180.u1.a1', '180.z1.a1', '180.bc1.a1', '180.bm1.a1'], 'contains': ['720.c1.a1', '720.y1.a1', '720.ba1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8708, -1, 8786, -1, 9033, -1, 6171, -1], 'generators': [3669120, 8025247, 7], 'label': '2880.hl.360.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536900
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1.a1', '120.p1.a1', '180.c1.a1', '180.i1.a1', '180.x1.a1', '180.bb1.a1', '180.bc1.a1', '180.bd1.a1', '180.bk1.a1'], 'contains': ['720.c1.a1', '720.m1.a1', '720.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2988, -1, 3016, -1, 4563, -1, 5354, -1], 'generators': [23, 130, 3669143], 'label': '2880.hl.360.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536901
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.o1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1.a1', '120.q1.a1', '180.e1.a1', '180.k1.a1', '180.q1.a1', '180.v1.a1', '180.w1.a1', '180.bc1.a1', '180.bn1.a1'], 'contains': ['720.c1.a1', '720.bl1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7120, -1, 7517, -1, 8103, -1, 6850, -1], 'generators': [8023697, 3669120, 7], 'label': '2880.hl.360.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536902
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.p1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '120.r1.a1', '180.f1.a1', '180.j1.a1', '180.r1.a1', '180.u1.a1', '180.y1.a1', '180.bd1.a1', '180.bn1.a1'], 'contains': ['720.c1.a1', '720.z1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8902, -1, 9119, -1, 8657, -1, 5825, -1], 'generators': [3669120, 8023686, 7], 'label': '2880.hl.360.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536903
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.g1.a1', '6.p1.a1'], 'contains': ['24.n1.a1', '24.q1.a1', '24.w1.a1', '24.cl1.a1', '24.cm1.a1', '36.k1.a1', '60.j1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8128, -1, 8355, -1, 6724, -1, 8365, -1], 'generators': [3669960, 1456, 5, 8025134, 50803200, 16], 'label': '2880.hl.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183536904
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.q1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1.a1', '120.s1.a1', '180.d1.a1', '180.m1.a1', '180.o1.a1', '180.v1.a1', '180.ba1.a1', '180.bd1.a1', '180.bm1.a1'], 'contains': ['720.c1.a1', '720.ba1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8783, -1, 9148, -1, 8924, -1, 6712, -1], 'generators': [8025256, 3669120, 7], 'label': '2880.hl.360.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536905
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.r1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1.a1', '120.t1.a1', '180.f1.a1', '180.l1.a1', '180.q1.a1', '180.s1.a1', '180.ba1.a1', '180.bb1.a1', '180.bo1.a1'], 'contains': ['720.c1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8500, -1, 8600, -1, 8475, -1, 6135, -1], 'generators': [23, 8025261, 3669143], 'label': '2880.hl.360.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536906
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.s1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.a1', '120.u1.a1', '180.e1.a1', '180.m1.a1', '180.r1.a1', '180.t1.a1', '180.x1.a1', '180.z1.a1', '180.bo1.a1'], 'contains': ['720.c1.a1', '720.bm1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7592, -1, 7088, -1, 7895, -1, 6675, -1], 'generators': [23, 8025253, 3669143], 'label': '2880.hl.360.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536907
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '360.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1.a1', '120.v1.a1', '180.i1.a1', '180.be1.a1', '180.bh1.a1'], 'contains': ['720.d1.a1', '720.e1.a1', '720.m1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3164, -1, 2985, -1, 3138, -1, 3541, -1], 'generators': [127, 5, 16], 'label': '2880.hl.360.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '360.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536908
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.u1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1.a1', '120.w1.a1', '180.a1.a1', '180.be1.a1', '180.bp1.a1'], 'contains': ['720.d1.a1', '720.f1.a1', '720.k1.a1', '720.bd1.a1', '720.bf1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3434, -1, 3472, -1, 3416, -1, 3986, -1], 'generators': [5, 3669856, 16], 'label': '2880.hl.360.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536909
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '360.v1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1.a1', '120.x1.a1', '180.g1.a1', '180.be1.a1', '180.bj1.a1'], 'contains': ['720.d1.a1', '720.g1.a1', '720.n1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3694, -1, 3413, -1, 3332, -1, 3196, -1], 'generators': [5, 3669143, 16], 'label': '2880.hl.360.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536910
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.w1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1.a1', '120.y1.a1', '180.g1.a1', '180.i1.a1', '180.bp1.a1'], 'contains': ['720.d1.a1', '720.j1.a1', '720.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3282, -1, 3397, -1, 3157, -1, 3380, -1], 'generators': [5, 3669863, 16], 'label': '2880.hl.360.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536911
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.x1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1.a1', '120.z1.a1', '180.be1.a1', '180.bf1.a1', '180.bg1.a1'], 'contains': ['720.e1.a1', '720.f1.a1', '720.g1.a1', '720.bg1.a1', '720.bh1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4455, -1, 4578, -1, 3679, -1, 3891, -1], 'generators': [136, 3669143, 7], 'label': '2880.hl.360.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536912
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '360.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1.a1', '120.ba1.a1', '180.n1.a1', '180.bf1.a1', '180.bh1.a1'], 'contains': ['720.e1.a1', '720.h1.a1', '720.l1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2074, -1, 1943, -1, 2631, -1, 3851, -1], 'generators': [127, 9, 16], 'label': '2880.hl.360.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '360.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536913
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.z1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1.a1', '120.bb1.a1', '180.i1.a1', '180.bf1.a1', '180.bi1.a1'], 'contains': ['720.e1.a1', '720.i1.a1', '720.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2832, -1, 2213, -1, 2993, -1, 3812, -1], 'generators': [3669134, 127, 16], 'label': '2880.hl.360.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536914
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1', '6.p1.a1'], 'contains': ['24.n1.a1', '24.s1.a1', '24.v1.a1', '36.l1.a1', '60.k1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6939, -1, 7326, -1, 6925, -1, 7837, -1], 'generators': [3669960, 1456, 5, 8025138, 50803200, 16], 'label': '2880.hl.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}
  • id: 183536915
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.ba1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1.a1', '120.bc1.a1', '180.n1.a1', '180.be1.a1', '180.bi1.a1'], 'contains': ['720.e1.a1', '720.k1.a1', '720.n1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2340, -1, 2603, -1, 2677, -1, 3561, -1], 'generators': [3669138, 127, 16], 'label': '2880.hl.360.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536916
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bb1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1.a1', '120.bd1.a1', '180.a1.a1', '180.bf1.a1', '180.bq1.a1'], 'contains': ['720.f1.a1', '720.h1.a1', '720.i1.a1', '720.bj1.a1', '720.bn1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3221, -1, 2682, -1, 3244, -1, 4306, -1], 'generators': [3669134, 3669856, 16], 'label': '2880.hl.360.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536917
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bc1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1.a1', '120.be1.a1', '180.c1.a1', '180.bf1.a1', '180.bp1.a1'], 'contains': ['720.f1.a1', '720.l1.a1', '720.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1393, -1, 1622, -1, 1958, -1, 3784, -1], 'generators': [9, 3669856, 16], 'label': '2880.hl.360.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536918
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bd1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.be1.a1', '120.bf1.a1', '180.c1.a1', '180.be1.a1', '180.bq1.a1'], 'contains': ['720.f1.a1', '720.m1.a1', '720.n1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1448, -1, 1481, -1, 2023, -1, 3489, -1], 'generators': [3669138, 3669856, 16], 'label': '2880.hl.360.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536919
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.be1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bf1.a1', '120.bg1.a1', '180.g1.a1', '180.bf1.a1', '180.bk1.a1'], 'contains': ['720.g1.a1', '720.h1.a1', '720.o1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2235, -1, 2244, -1, 2793, -1, 3259, -1], 'generators': [23, 122, 3669136], 'label': '2880.hl.360.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536920
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '360.bf1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bg1.a1', '120.bh1.a1', '180.h1.a1', '180.bf1.a1', '180.bj1.a1'], 'contains': ['720.g1.a1', '720.i1.a1', '720.l1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2724, -1, 1849, -1, 2974, -1, 3580, -1], 'generators': [9, 3669143, 16], 'label': '2880.hl.360.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536921
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.bg1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bh1.a1', '120.bi1.a1', '180.h1.a1', '180.be1.a1', '180.bk1.a1'], 'contains': ['720.g1.a1', '720.k1.a1', '720.m1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2356, -1, 2789, -1, 2585, -1, 3339, -1], 'generators': [23, 130, 3669136], 'label': '2880.hl.360.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536922
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.bh1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1.a1', '120.bj1.a1', '180.g1.a1', '180.n1.a1', '180.bq1.a1'], 'contains': ['720.h1.a1', '720.j1.a1', '720.n1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2258, -1, 2229, -1, 2887, -1, 3400, -1], 'generators': [3669138, 3669863, 16], 'label': '2880.hl.360.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536923
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.bi1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bj1.a1', '120.bk1.a1', '180.h1.a1', '180.i1.a1', '180.bq1.a1'], 'contains': ['720.i1.a1', '720.j1.a1', '720.m1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2679, -1, 2197, -1, 3012, -1, 3636, -1], 'generators': [3669134, 3669863, 16], 'label': '2880.hl.360.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536924
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.bj1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bk1.a1', '120.bl1.a1', '180.h1.a1', '180.n1.a1', '180.bp1.a1'], 'contains': ['720.j1.a1', '720.k1.a1', '720.l1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2126, -1, 2523, -1, 2467, -1, 3711, -1], 'generators': [9, 3669863, 16], 'label': '2880.hl.360.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536925
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.h1.a1', '6.q1.a1'], 'contains': ['24.n1.a1', '24.t1.a1', '24.y1.a1', '24.cn1.a1', '24.co1.a1', '36.m1.a1', '60.l1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8848, -1, 8748, -1, 6833, -1, 8418, -1], 'generators': [3669960, 1456, 5, 8025254, 50803200, 16], 'label': '2880.hl.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536926
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '360.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bl1.a1', '120.a1.a1', '120.bm1.a1', '180.bg1.a1', '180.bh1.a1', '180.bi1.a1'], 'contains': ['720.a1.a1', '720.b1.a1', '720.e1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2299, -1, 1675, -1, 1147, -1, 2704, -1], 'generators': [127, 23, 7], 'label': '2880.hl.360.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '360.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536927
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.bl1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '30.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.bn1.a1', '120.bo1.a1', '120.bp1.a1', '180.bg1.a1', '180.bj1.a1', '180.bk1.a1', '180.bl1.a1', '180.bm1.a1', '180.bn1.a1', '180.bo1.a1'], 'contains': ['720.a1.a1', '720.c1.a1', '720.g1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4931, -1, 4904, -1, 4817, -1, 3360, -1], 'generators': [23, 3669143, 7], 'label': '2880.hl.360.bl1.a1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '360.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536928
    {'ambient': '2880.hl', 'aut_centralizer_order': 240, 'aut_label': '360.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bm1.a1', '120.b1.a1', '120.bq1.a1', '180.bh1.a1', '180.bj1.a1', '180.bp1.a1'], 'contains': ['720.a1.a1', '720.d1.a1', '720.l1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1140, -1, 1130, -1, 1035, -1, 2664, -1], 'generators': [23, 5, 7], 'label': '2880.hl.360.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '360.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536929
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bn1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bn1.a1', '120.br1.a1', '120.bs1.a1', '180.bg1.a1', '180.bp1.a1', '180.bq1.a1'], 'contains': ['720.a1.a1', '720.f1.a1', '720.j1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1473, -1, 2456, -1, 1505, -1, 2643, -1], 'generators': [23, 3669863, 7], 'label': '2880.hl.360.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '360.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536930
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '360.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1.a1', '120.bt1.a1', '120.bu1.a1', '120.bv1.a1', '180.bh1.a1', '180.bk1.a1', '180.bq1.a1'], 'contains': ['720.a1.a1', '720.h1.a1', '720.m1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1156, -1, 1145, -1, 904, -1, 2623, -1], 'generators': [23, 122, 7], 'label': '2880.hl.360.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '360.bo1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536931
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '360.bp1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1.a1', '120.bw1.a1', '120.bx1.a1', '180.bi1.a1', '180.bj1.a1', '180.bq1.a1'], 'contains': ['720.a1.a1', '720.i1.a1', '720.n1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1333, -1, 1202, -1, 1054, -1, 2683, -1], 'generators': [3669138, 23, 7], 'label': '2880.hl.360.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '360.bp1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536932
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '360.bq1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 720, 'centralizer': '180.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1.a1', '120.by1.a1', '120.bz1.a1', '120.ca1.a1', '180.bi1.a1', '180.bk1.a1', '180.bp1.a1'], 'contains': ['720.a1.a1', '720.k1.a1', '720.o1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [1196, -1, 1217, -1, 885, -1, 2602, -1], 'generators': [23, 3669850, 7], 'label': '2880.hl.360.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bq1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 183536933
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.br1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1.a1', '120.cb1.a1', '120.ce1.a1', '180.a1.a1', '180.br1.a1', '180.bs1.a1'], 'contains': ['720.p1.a1', '720.q1.a1', '720.s1.a1', '720.t1.a1', '720.v1.a1', '720.bd1.a1', '720.bj1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4396, -1, 4475, -1, 5013, -1, 7266, -1], 'generators': [5, 3669120, 120], 'label': '2880.hl.360.br1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.br1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.br1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536934
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '360.bs1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bs1.a1', '120.cc1.a1', '120.cf1.a1', '180.b1.a1', '180.br1.a1'], 'contains': ['720.p1.a1', '720.w1.a1', '720.y1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7985, -1, 8126, -1, 8257, -1, 6079, -1], 'generators': [3669120, 8023680, 120], 'label': '2880.hl.360.bs1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '360.bs1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536935
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '360.bt1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1.a1', '120.cg1.a1', '180.b1.a1', '180.d1.a1', '180.bs1.a1'], 'contains': ['720.p1.a1', '720.x1.a1', '720.ba1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9780, -1, 9769, -1, 9385, -1, 7295, -1], 'generators': [3669120, 8023687, 120], 'label': '2880.hl.360.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.bt1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536936
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.g1.a1', '6.q1.a1'], 'contains': ['24.n1.a1', '24.x1.a1', '24.z1.a1', '36.n1.a1', '60.m1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7424, -1, 6671, -1, 7702, -1, 7789, -1], 'generators': [3669960, 1456, 5, 8025258, 50803200, 16], 'label': '2880.hl.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536937
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bu1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bu1.a1', '120.cd1.a1', '120.ch1.a1', '180.f1.a1', '180.br1.a1', '180.bs1.a1'], 'contains': ['720.p1.a1', '720.z1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8969, -1, 9263, -1, 8390, -1, 6542, -1], 'generators': [3669120, 8023686, 120], 'label': '2880.hl.360.bu1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.bu1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536938
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bv1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bv1.a1', '120.ci1.a1', '180.a1.a1'], 'contains': ['720.q1.a1', '720.r1.a1', '720.s1.a1', '720.be1.a1', '720.bf1.a1', '720.bk1.a1', '720.bn1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5048, -1, 5022, -1, 5057, -1, 8068, -1], 'generators': [5, 3669136, 120], 'label': '2880.hl.360.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.bv1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536939
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bw1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bw1.a1', '120.cj1.a1', '180.e1.a1'], 'contains': ['720.r1.a1', '720.bl1.a1', '720.bm1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6794, -1, 6831, -1, 7141, -1, 8310, -1], 'generators': [8023697, 3669127, 120], 'label': '2880.hl.360.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.bw1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536940
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.bx1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bx1.a1', '120.ck1.a1', '180.a1.a1', '180.bt1.a1', '180.bu1.a1'], 'contains': ['720.t1.a1', '720.u1.a1', '720.v1.a1', '720.bc1.a1', '720.bf1.a1', '720.bi1.a1', '720.bn1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5450, -1, 5424, -1, 5322, -1, 7707, -1], 'generators': [136, 5, 3669120], 'label': '2880.hl.360.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.bx1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536941
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.by1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1.a1', '120.cl1.a1', '120.cp1.a1', '180.j1.a1', '180.br1.a1', '180.bt1.a1'], 'contains': ['720.t1.a1', '720.w1.a1', '720.z1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8066, -1, 8436, -1, 8317, -1, 6974, -1], 'generators': [5, 8023685, 3669120], 'label': '2880.hl.360.by1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '360.by1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.by1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536942
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '360.bz1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1.a1', '120.cm1.a1', '180.j1.a1', '180.bs1.a1', '180.bu1.a1'], 'contains': ['720.t1.a1', '720.x1.a1', '720.z1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9537, -1, 9668, -1, 8997, -1, 7502, -1], 'generators': [8023694, 5, 3669120], 'label': '2880.hl.360.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '360.bz1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536943
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.ca1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ca1.a1', '120.cn1.a1', '120.cq1.a1', '180.l1.a1', '180.br1.a1', '180.bu1.a1'], 'contains': ['720.t1.a1', '720.y1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8821, -1, 8678, -1, 8353, -1, 7011, -1], 'generators': [5, 8025245, 3669120], 'label': '2880.hl.360.ca1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.ca1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536944
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.cb1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cb1.a1', '120.co1.a1', '180.l1.a1', '180.bs1.a1', '180.bt1.a1'], 'contains': ['720.t1.a1', '720.ba1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9231, -1, 9563, -1, 8960, -1, 7331, -1], 'generators': [5, 8025254, 3669120], 'label': '2880.hl.360.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.cb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536945
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '360.cc1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1.a1', '120.cr1.a1', '180.b1.a1', '180.o1.a1', '180.bt1.a1'], 'contains': ['720.u1.a1', '720.w1.a1', '720.ba1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8406, -1, 8556, -1, 9243, -1, 7119, -1], 'generators': [127, 3669120, 8023680], 'label': '2880.hl.360.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.cc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536946
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '360.cd1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cd1.a1', '120.cs1.a1', '180.b1.a1', '180.p1.a1', '180.bu1.a1'], 'contains': ['720.u1.a1', '720.x1.a1', '720.y1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9157, -1, 9486, -1, 9282, -1, 7368, -1], 'generators': [127, 3669120, 8023687], 'label': '2880.hl.360.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '360.cd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536947
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.j1.a1', '6.n1.a1'], 'contains': ['24.o1.a1', '24.p1.a1', '24.r1.a1', '24.bf1.a1', '24.bh1.a1', '24.bo1.a1', '24.bq1.a1', '36.o1.a1', '60.n1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2501, -1, 3319, -1, 3239, -1, 5168, -1], 'generators': [127, 3669960, 1456, 9, 50803200, 16], 'label': '2880.hl.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536948
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.ce1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ce1.a1', '120.ct1.a1', '180.d1.a1', '180.o1.a1', '180.p1.a1'], 'contains': ['720.u1.a1', '720.x1.a1', '720.ba1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9746, -1, 9698, -1, 9537, -1, 7404, -1], 'generators': [127, 3669120, 8023696], 'label': '2880.hl.360.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.j1.a1', 'old_label': '360.ce1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536949
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.cf1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cf1.a1', '120.cu1.a1', '180.f1.a1', '180.bt1.a1', '180.bu1.a1'], 'contains': ['720.u1.a1', '720.z1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9189, -1, 9528, -1, 8749, -1, 7200, -1], 'generators': [127, 3669120, 8023686], 'label': '2880.hl.360.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.cf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536950
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.cg1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cg1.a1', '120.cv1.a1', '120.cz1.a1', '120.db1.a1', '180.s1.a1', '180.br1.a1', '180.bt1.a1'], 'contains': ['720.v1.a1', '720.w1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8159, -1, 8174, -1, 8221, -1, 6505, -1], 'generators': [3669120, 8025261, 8023680], 'label': '2880.hl.360.cg1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.cg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536951
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.ch1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ch1.a1', '120.cw1.a1', '180.s1.a1', '180.bs1.a1', '180.bu1.a1'], 'contains': ['720.v1.a1', '720.x1.a1', '720.bb1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9354, -1, 9610, -1, 8842, -1, 7441, -1], 'generators': [8023703, 3669120, 8025261], 'label': '2880.hl.360.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.ch1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536952
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.ci1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ci1.a1', '120.cx1.a1', '120.da1.a1', '180.u1.a1', '180.br1.a1', '180.bu1.a1'], 'contains': ['720.v1.a1', '720.y1.a1', '720.z1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8746, -1, 9178, -1, 8512, -1, 6938, -1], 'generators': [8023682, 122, 3669120], 'label': '2880.hl.360.ci1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.ci1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536953
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.cj1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cj1.a1', '120.cy1.a1', '180.u1.a1', '180.bs1.a1', '180.bt1.a1'], 'contains': ['720.v1.a1', '720.z1.a1', '720.ba1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9265, -1, 9639, -1, 9073, -1, 7236, -1], 'generators': [122, 3669120, 8023701], 'label': '2880.hl.360.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.cj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536954
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.ck1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1.a1', '120.dc1.a1', '180.a1.a1'], 'contains': ['720.bc1.a1', '720.bd1.a1', '720.be1.a1', '720.bg1.a1', '720.bi1.a1', '720.bj1.a1', '720.bk1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5066, -1, 5088, -1, 5035, -1, 7971, -1], 'generators': [136, 5, 3669136], 'label': '2880.hl.360.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.ck1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536955
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '360.cl1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cl1.a1', '120.dd1.a1', '180.e1.a1'], 'contains': ['720.bg1.a1', '720.bl1.a1', '720.bm1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6731, -1, 6802, -1, 7105, -1, 8188, -1], 'generators': [127, 8023697, 3669127], 'label': '2880.hl.360.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.cl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536956
    {'ambient': '2880.hl', 'aut_centralizer_order': 480, 'aut_label': '480.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '6.b1.a1', 'complements': ['6.b1.a1', '6.r1.a1', '6.u1.a1', '6.w1.a1', '6.v1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.a1.a1', '240.c1.a1', '240.u1.a1', '240.v1.a1', '240.w1.a1', '240.x1.a1'], 'contains': ['960.a1.a1', '1440.b1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4200, 4899, 4216, 4547, 4461, 4441, 7359, 5774], 'generators': [1440, 120], 'label': '2880.hl.480.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '480.a1.a1', 'normal_contained_in': ['96.a1.a1', '120.a1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '1.1', 'quotient_action_kernel': '480.1189', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536957
    {'ambient': '2880.hl', 'aut_centralizer_order': 480, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '6.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '240.a1.a1', '240.c1.a1', '240.d1.a1', '240.e1.a1', '240.f1.a1', '240.g1.a1', '240.h1.a1', '240.i1.a1', '240.j1.a1', '240.k1.a1', '240.l1.a1', '240.m1.a1', '240.n1.a1', '240.o1.a1', '240.p1.a1'], 'contains': ['960.a1.a1', '1440.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3703, -1, 3627, -1, 3504, -1, 3829, -1], 'generators': [1447, 7], 'label': '2880.hl.480.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '480.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536958
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.g1.a1', '6.i1.a1'], 'contains': ['24.o1.a1', '24.q1.a1', '24.x1.a1', '24.cr1.a1', '24.ct1.a1', '36.p1.a1', '60.o1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8371, -1, 8412, -1, 7753, -1, 8196, -1], 'generators': [136, 8025127, 3669967, 1447, 50803200, 7], 'label': '2880.hl.12.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536959
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '24.cd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '120.bm1.a1', '160.a1.a1', '240.r1.a1', '240.s1.a1', '240.t1.a1'], 'contains': ['960.b1.a1', '1440.b1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1816, -1, 1256, -1, 936, -1, 965, -1], 'generators': [124, 3], 'label': '2880.hl.480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '480.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536960
    {'ambient': '2880.hl', 'aut_centralizer_order': 288, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '10.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '160.b1.a1', '240.d1.a1', '240.u1.a1', '240.y1.a1', '240.ba1.a1', '240.bb1.a1', '240.be1.a1', '240.bf1.a1', '240.bg1.a1', '240.bh1.a1', '240.bi1.a1', '240.bj1.a1'], 'contains': ['960.a1.a1', '1440.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6577, -1, 6749, -1, 6527, -1, 7276, -1], 'generators': [1440, 3669960], 'label': '2880.hl.480.d1.a1', 'mobius_quo': None, 'mobius_sub': 96, 'normal_closure': '96.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '480.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536961
    {'ambient': '2880.hl', 'aut_centralizer_order': 72, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '40.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '120.bo1.a1', '160.b1.a1', '240.r1.a1', '240.z1.a1', '240.bc1.a1', '240.bk1.a1', '240.bl1.a1', '240.bm1.a1', '240.bn1.a1'], 'contains': ['960.b1.a1', '1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [4243, -1, 4250, -1, 4623, -1, 1571, -1], 'generators': [11, 3669120], 'label': '2880.hl.480.e1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '480.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536962
    {'ambient': '2880.hl', 'aut_centralizer_order': 36, 'aut_label': '480.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '80.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '120.bp1.a1', '160.b1.a1', '240.bd1.a1', '240.bo1.a1', '240.bp1.a1'], 'contains': ['960.c1.a1', '1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [4260, -1, 4332, -1, 4869, -1, 1754, -1], 'generators': [1443, 3669964], 'label': '2880.hl.480.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.m1.a1', 'old_label': '480.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536963
    {'ambient': '2880.hl', 'aut_centralizer_order': 240, 'aut_label': '480.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '12.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '160.c1.a1', '240.e1.a1', '240.v1.a1', '240.y1.a1', '240.bq1.a1', '240.br1.a1', '240.bs1.a1', '240.bt1.a1'], 'contains': ['960.a1.a1', '1440.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5237, -1, 5296, -1, 4784, -1, 7588, -1], 'generators': [1440, 5], 'label': '2880.hl.480.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '480.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536964
    {'ambient': '2880.hl', 'aut_centralizer_order': 120, 'aut_label': '480.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '24.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '120.b1.a1', '160.c1.a1', '240.s1.a1', '240.z1.a1', '240.bu1.a1'], 'contains': ['960.b1.a1', '1440.d1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2934, -1, 2772, -1, 1387, -1, 846, -1], 'generators': [11, 5], 'label': '2880.hl.480.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '480.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536965
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '480.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1', '240.c1.a1', '240.f1.a1', '240.ba1.a1', '240.bq1.a1', '240.bv1.a1', '240.bw1.a1', '240.bx1.a1'], 'contains': ['960.a1.a1', '1440.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5531, -1, 5513, -1, 5144, -1, 7530, -1], 'generators': [127, 1440], 'label': '2880.hl.480.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '480.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536966
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '480.j1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '120.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '120.br1.a1', '160.d1.a1', '240.r1.a1', '240.bu1.a1', '240.by1.a1'], 'contains': ['960.b1.a1', '1440.f1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1801, -1, 1608, -1, 1082, -1, 768, -1], 'generators': [12, 3669848], 'label': '2880.hl.480.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '480.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536967
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '480.k1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '30.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '160.d1.a1', '240.g1.a1', '240.u1.a1', '240.br1.a1', '240.bv1.a1', '240.bz1.a1'], 'contains': ['960.a1.a1', '1440.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4095, -1, 4317, -1, 4480, -1, 7340, -1], 'generators': [1440, 3669840], 'label': '2880.hl.480.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '480.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536968
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '480.l1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.l1.a1', '240.d1.a1', '240.h1.a1', '240.w1.a1', '240.bs1.a1', '240.bv1.a1', '240.bw1.a1', '240.ca1.a1', '240.cb1.a1', '240.cc1.a1'], 'contains': ['960.a1.a1', '1440.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5730, -1, 5864, -1, 5717, -1, 7887, -1], 'generators': [1440, 3669967], 'label': '2880.hl.480.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '480.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536969
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 6, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1', '6.r1.a1', '6.u1.a1', '6.v1.a1', '9.a1.a1', '12.cf1.a1', '15.a1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5716, -1, 5970, -1, 4995, -1, 2387, -1], 'generators': [11, 124, 23, 8023697, 5, 3669143, 50803200, 7], 'label': '2880.hl.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': '2880.hl', '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': '480.1189'}
  • id: 183536970
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.o1.a1', '24.s1.a1', '24.t1.a1', '24.cs1.a1', '24.ct1.a1', '36.q1.a1', '60.p1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9393, -1, 8961, -1, 7809, -1, 8140, -1], 'generators': [136, 3669967, 8025136, 1447, 50803200, 7], 'label': '2880.hl.12.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183536971
    {'ambient': '2880.hl', 'aut_centralizer_order': 80, 'aut_label': '480.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.m1.a1', '160.e1.a1', '240.i1.a1', '240.v1.a1', '240.bb1.a1', '240.bq1.a1', '240.bz1.a1', '240.ca1.a1', '240.cd1.a1'], 'contains': ['960.a1.a1', '1440.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4395, -1, 4549, -1, 4561, -1, 7569, -1], 'generators': [1440, 122], 'label': '2880.hl.480.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '480.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536972
    {'ambient': '2880.hl', 'aut_centralizer_order': 40, 'aut_label': '480.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '72.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.a1', '120.bu1.a1', '160.e1.a1', '240.s1.a1', '240.bc1.a1', '240.by1.a1'], 'contains': ['960.b1.a1', '1440.h1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1934, -1, 1706, -1, 1341, -1, 944, -1], 'generators': [122, 12], 'label': '2880.hl.480.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '480.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536973
    {'ambient': '2880.hl', 'aut_centralizer_order': 20, 'aut_label': '480.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1.a1', '120.bv1.a1', '160.e1.a1', '240.bd1.a1'], 'contains': ['960.c1.a1', '1440.h1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1958, -1, 1722, -1, 1367, -1, 1177, -1], 'generators': [122, 1443], 'label': '2880.hl.480.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.db1.a1', 'old_label': '480.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536974
    {'ambient': '2880.hl', 'aut_centralizer_order': 48, 'aut_label': '480.p1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '160.f1.a1', '240.j1.a1', '240.x1.a1', '240.y1.a1', '240.bs1.a1', '240.bx1.a1', '240.bz1.a1', '240.cd1.a1'], 'contains': ['960.a1.a1', '1440.i1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5159, -1, 4864, -1, 4642, -1, 7607, -1], 'generators': [1440, 3669974], 'label': '2880.hl.480.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '480.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536975
    {'ambient': '2880.hl', 'aut_centralizer_order': 24, 'aut_label': '480.q1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '120.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.a1', '120.bx1.a1', '160.f1.a1', '240.t1.a1', '240.z1.a1', '240.by1.a1'], 'contains': ['960.b1.a1', '1440.i1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2061, -1, 1745, -1, 1257, -1, 893, -1], 'generators': [11, 3669125], 'label': '2880.hl.480.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.l1.a1', 'old_label': '480.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536976
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '480.r1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '90.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1.a1', '240.g1.a1', '240.k1.a1', '240.w1.a1', '240.ba1.a1', '240.bt1.a1', '240.bw1.a1', '240.cd1.a1'], 'contains': ['960.a1.a1', '1440.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5359, -1, 5498, -1, 5169, -1, 7627, -1], 'generators': [1440, 3669863], 'label': '2880.hl.480.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '480.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536977
    {'ambient': '2880.hl', 'aut_centralizer_order': 16, 'aut_label': '480.s1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '180.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.s1.a1', '160.g1.a1', '240.l1.a1', '240.x1.a1', '240.bb1.a1', '240.br1.a1', '240.bt1.a1', '240.bx1.a1', '240.ca1.a1'], 'contains': ['960.a1.a1', '1440.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4601, -1, 5280, -1, 4542, -1, 7549, -1], 'generators': [1440, 3669842], 'label': '2880.hl.480.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '480.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.s1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536978
    {'ambient': '2880.hl', 'aut_centralizer_order': 8, 'aut_label': '480.t1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '360.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.t1.a1', '120.bz1.a1', '160.g1.a1', '240.t1.a1', '240.bc1.a1', '240.bu1.a1'], 'contains': ['960.b1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2046, -1, 2062, -1, 1172, -1, 811, -1], 'generators': [3669842, 12], 'label': '2880.hl.480.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.cf1.a1', 'old_label': '480.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536979
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '480.u1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '720.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.u1.a1', '120.ca1.a1', '160.g1.a1', '240.bd1.a1'], 'contains': ['960.c1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [2648, -1, 2440, -1, 1238, -1, 1158, -1], 'generators': [1443, 3669842], 'label': '2880.hl.480.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.db1.a1', 'old_label': '480.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536980
    {'ambient': '2880.hl', 'aut_centralizer_order': 720, 'aut_label': '576.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 720, 'centralizer': '4.b1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.c1.a1', '288.a1.a1', '288.b1.a1', '288.c1.a1', '288.d1.a1', '288.e1.a1', '288.f1.a1', '288.g1.a1', '288.h1.a1', '288.i1.a1', '288.j1.a1', '288.k1.a1'], 'contains': ['2880.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4942, 4053, 4549, 3710, 4441, 4813, 8115, 5402], 'generators': [50803200], 'label': '2880.hl.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['144.a1.a1', '192.a1.a1', '288.a1.a1'], 'normal_contains': ['2880.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '4.1', 'quotient_action_kernel': '144.183', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 183536981
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.o1.a1', '24.v1.a1', '24.y1.a1', '36.r1.a1', '60.q1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6989, -1, 7080, -1, 6223, -1, 7548, -1], 'generators': [136, 3669967, 1447, 8025137, 50803200, 7], 'label': '2880.hl.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536982
    {'ambient': '2880.hl', 'aut_centralizer_order': 480, 'aut_label': '720.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 480, 'centralizer': '6.a1.a1', 'complements': ['4.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.a1.a1', '240.b1.a1', '240.q1.a1', '360.bk1.a1', '360.bl1.a1', '360.bm1.a1', '360.bn1.a1', '360.bo1.a1', '360.bp1.a1', '360.bq1.a1'], 'contains': ['1440.a1.a1'], 'core': '720.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1354, 5702, 1209, 5791, 1126, 3572, 2653, 6400], 'generators': [23, 7], 'label': '2880.hl.720.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '720.a1.a1', 'normal_contained_in': ['144.a1.a1', '240.a1.a1', '240.b1.a1'], 'normal_contains': ['2880.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '720.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '6.1', 'quotient_action_kernel': '120.36', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 183536983
    {'ambient': '2880.hl', 'aut_centralizer_order': 320, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '240.c1.a1', '360.a1.a1', '360.b1.a1', '360.c1.a1', '360.d1.a1', '360.e1.a1', '360.f1.a1', '360.bk1.a1'], 'contains': ['1440.a1.a1', '1440.b1.a1', '1440.e1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3383, -1, 2930, -1, 3194, -1, 3968, -1], 'generators': [127, 7], 'label': '2880.hl.720.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '720.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536984
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.d1.a1', '360.a1.a1', '360.g1.a1', '360.h1.a1', '360.i1.a1', '360.j1.a1', '360.k1.a1', '360.l1.a1', '360.m1.a1', '360.n1.a1', '360.o1.a1', '360.p1.a1', '360.q1.a1', '360.r1.a1', '360.s1.a1', '360.bl1.a1'], 'contains': ['1440.a1.a1', '1440.c1.a1', '1440.g1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6642, -1, 6798, -1, 6507, -1, 6434, -1], 'generators': [3669120, 7], 'label': '2880.hl.720.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '720.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536985
    {'ambient': '2880.hl', 'aut_centralizer_order': 480, 'aut_label': '720.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.e1.a1', '360.b1.a1', '360.g1.a1', '360.t1.a1', '360.u1.a1', '360.v1.a1', '360.w1.a1', '360.bm1.a1'], 'contains': ['1440.a1.a1', '1440.d1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3446, -1, 3475, -1, 3383, -1, 3764, -1], 'generators': [5, 16], 'label': '2880.hl.720.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '720.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536986
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '720.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '240.f1.a1', '360.h1.a1', '360.t1.a1', '360.x1.a1', '360.y1.a1', '360.z1.a1', '360.ba1.a1', '360.bk1.a1'], 'contains': ['1440.a1.a1', '1440.e1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3518, -1, 2999, -1, 3216, -1, 3850, -1], 'generators': [136, 7], 'label': '2880.hl.720.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '720.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536987
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '720.f1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.a1', '240.g1.a1', '360.a1.a1', '360.u1.a1', '360.x1.a1', '360.bb1.a1', '360.bc1.a1', '360.bd1.a1', '360.bn1.a1'], 'contains': ['1440.a1.a1', '1440.f1.a1', '1440.j1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3237, -1, 2972, -1, 3266, -1, 4000, -1], 'generators': [3669840, 7], 'label': '2880.hl.720.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536988
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '720.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.h1.a1', '240.h1.a1', '360.c1.a1', '360.v1.a1', '360.x1.a1', '360.be1.a1', '360.bf1.a1', '360.bg1.a1', '360.bl1.a1'], 'contains': ['1440.a1.a1', '1440.g1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4364, -1, 4525, -1, 3656, -1, 3568, -1], 'generators': [3669143, 7], 'label': '2880.hl.720.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '720.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536989
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '720.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.i1.a1', '240.i1.a1', '360.b1.a1', '360.i1.a1', '360.y1.a1', '360.bb1.a1', '360.be1.a1', '360.bh1.a1', '360.bo1.a1'], 'contains': ['1440.a1.a1', '1440.h1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3044, -1, 2703, -1, 3150, -1, 3939, -1], 'generators': [23, 122], 'label': '2880.hl.720.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '720.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536990
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '720.i1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.a1', '240.j1.a1', '360.d1.a1', '360.g1.a1', '360.z1.a1', '360.bb1.a1', '360.bf1.a1', '360.bi1.a1', '360.bp1.a1'], 'contains': ['1440.a1.a1', '1440.i1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3205, -1, 2666, -1, 3172, -1, 4035, -1], 'generators': [3669134, 16], 'label': '2880.hl.720.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '720.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536991
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.j1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.k1.a1', '240.k1.a1', '360.c1.a1', '360.h1.a1', '360.w1.a1', '360.bh1.a1', '360.bi1.a1', '360.bj1.a1', '360.bn1.a1'], 'contains': ['1440.a1.a1', '1440.j1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3465, -1, 3405, -1, 3288, -1, 3711, -1], 'generators': [3669863, 7], 'label': '2880.hl.720.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536992
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.j1.a1', '6.o1.a1'], 'contains': ['24.o1.a1', '24.w1.a1', '24.z1.a1', '36.s1.a1', '60.r1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7387, -1, 6960, -1, 6442, -1, 7390, -1], 'generators': [136, 3669967, 1447, 8025126, 50803200, 7], 'label': '2880.hl.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183536993
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.k1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.l1.a1', '240.l1.a1', '360.d1.a1', '360.i1.a1', '360.u1.a1', '360.ba1.a1', '360.bg1.a1', '360.bj1.a1', '360.bq1.a1'], 'contains': ['1440.a1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3111, -1, 2948, -1, 3105, -1, 3872, -1], 'generators': [23, 3669842], 'label': '2880.hl.720.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536994
    {'ambient': '2880.hl', 'aut_centralizer_order': 480, 'aut_label': '720.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1.a1', '240.m1.a1', '360.e1.a1', '360.k1.a1', '360.y1.a1', '360.bc1.a1', '360.bf1.a1', '360.bj1.a1', '360.bm1.a1'], 'contains': ['1440.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1865, -1, 1800, -1, 2528, -1, 3784, -1], 'generators': [9, 16], 'label': '2880.hl.720.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '720.l1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536995
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '720.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.n1.a1', '240.n1.a1', '360.e1.a1', '360.n1.a1', '360.t1.a1', '360.bd1.a1', '360.bg1.a1', '360.bi1.a1', '360.bo1.a1'], 'contains': ['1440.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1944, -1, 2037, -1, 2666, -1, 3608, -1], 'generators': [23, 130], 'label': '2880.hl.720.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '720.m1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536996
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '720.n1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '30.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1.a1', '240.o1.a1', '360.f1.a1', '360.k1.a1', '360.v1.a1', '360.ba1.a1', '360.bd1.a1', '360.bh1.a1', '360.bp1.a1'], 'contains': ['1440.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2270, -1, 2136, -1, 2849, -1, 3444, -1], 'generators': [3669138, 16], 'label': '2880.hl.720.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '720.n1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536997
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.o1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.p1.a1', '240.p1.a1', '360.f1.a1', '360.n1.a1', '360.w1.a1', '360.z1.a1', '360.bc1.a1', '360.be1.a1', '360.bq1.a1'], 'contains': ['1440.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [2033, -1, 2189, -1, 2782, -1, 3589, -1], 'generators': [23, 3669850], 'label': '2880.hl.720.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.o1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183536998
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '720.p1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1.a1', '240.r1.a1', '240.u1.a1', '360.a1.a1', '360.br1.a1', '360.bs1.a1', '360.bt1.a1', '360.bu1.a1'], 'contains': ['1440.b1.a1', '1440.c1.a1', '1440.f1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4339, -1, 4462, -1, 5080, -1, 7148, -1], 'generators': [3669120, 120], 'label': '2880.hl.720.p1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '720.p1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183536999
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '720.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1.a1', '240.s1.a1', '240.v1.a1', '360.b1.a1', '360.br1.a1', '360.bv1.a1'], 'contains': ['1440.b1.a1', '1440.d1.a1', '1440.h1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4207, -1, 4284, -1, 4440, -1, 7402, -1], 'generators': [5, 120], 'label': '2880.hl.720.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '720.q1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537000
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '720.r1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1.a1', '240.w1.a1', '360.a1.a1', '360.c1.a1', '360.bv1.a1', '360.bw1.a1'], 'contains': ['1440.b1.a1', '1440.g1.a1', '1440.j1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5639, -1, 5753, -1, 5481, -1, 7908, -1], 'generators': [3669143, 120], 'label': '2880.hl.720.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.r1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.r1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537001
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.s1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.t1.a1', '240.t1.a1', '240.x1.a1', '360.d1.a1', '360.br1.a1', '360.bv1.a1'], 'contains': ['1440.b1.a1', '1440.i1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4275, -1, 4371, -1, 4374, -1, 7468, -1], 'generators': [3669125, 120], 'label': '2880.hl.720.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.s1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.s1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537002
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '720.t1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1.a1', '240.y1.a1', '240.z1.a1', '360.g1.a1', '360.br1.a1', '360.bx1.a1', '360.by1.a1', '360.bz1.a1', '360.ca1.a1', '360.cb1.a1'], 'contains': ['1440.c1.a1', '1440.d1.a1', '1440.i1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5711, -1, 5973, -1, 6348, -1, 7424, -1], 'generators': [5, 3669120], 'label': '2880.hl.720.t1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '720.t1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537003
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.i1.a1', '6.s1.a1'], 'contains': ['24.p1.a1', '24.q1.a1', '24.y1.a1', '24.cv1.a1', '24.cw1.a1', '36.t1.a1', '60.s1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8317, -1, 8199, -1, 6402, -1, 8471, -1], 'generators': [23, 3669960, 8025143, 1463, 8025261, 50803200], 'label': '2880.hl.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183537004
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '720.u1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1.a1', '240.ba1.a1', '360.a1.a1', '360.h1.a1', '360.bx1.a1', '360.cc1.a1', '360.cd1.a1', '360.ce1.a1', '360.cf1.a1'], 'contains': ['1440.c1.a1', '1440.e1.a1', '1440.j1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6468, -1, 6605, -1, 6548, -1, 7490, -1], 'generators': [127, 3669120], 'label': '2880.hl.720.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.u1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.u1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537005
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.v1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.w1.a1', '240.bb1.a1', '240.bc1.a1', '240.bd1.a1', '360.i1.a1', '360.br1.a1', '360.bx1.a1', '360.cg1.a1', '360.ch1.a1', '360.ci1.a1', '360.cj1.a1'], 'contains': ['1440.c1.a1', '1440.h1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4891, -1, 5417, -1, 5101, -1, 7236, -1], 'generators': [122, 3669120], 'label': '2880.hl.720.v1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.v1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.v1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537006
    {'ambient': '2880.hl', 'aut_centralizer_order': 576, 'aut_label': '720.w1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '240.be1.a1', '240.bk1.a1', '240.bo1.a1', '360.j1.a1', '360.bs1.a1', '360.by1.a1', '360.cc1.a1', '360.cg1.a1'], 'contains': ['1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7997, -1, 7989, -1, 8239, -1, 6740, -1], 'generators': [3669120, 8023680], 'label': '2880.hl.720.w1.a1', 'mobius_quo': None, 'mobius_sub': 72, 'normal_closure': '144.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '720.w1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.w1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537007
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '720.x1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.x1.a1', '240.bf1.a1', '360.j1.a1', '360.l1.a1', '360.bt1.a1', '360.bz1.a1', '360.cd1.a1', '360.ce1.a1', '360.ch1.a1'], 'contains': ['1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9345, -1, 9623, -1, 8919, -1, 7511, -1], 'generators': [3669120, 8023696], 'label': '2880.hl.720.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '720.x1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.x1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537008
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '720.y1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.y1.a1', '240.bg1.a1', '240.bl1.a1', '360.m1.a1', '360.bs1.a1', '360.ca1.a1', '360.cd1.a1', '360.ci1.a1'], 'contains': ['1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8238, -1, 8509, -1, 8373, -1, 7011, -1], 'generators': [3669120, 8025240], 'label': '2880.hl.720.y1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '720.y1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.y1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537009
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '720.z1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.z1.a1', '240.bh1.a1', '240.bm1.a1', '360.p1.a1', '360.bu1.a1', '360.by1.a1', '360.bz1.a1', '360.cf1.a1', '360.ci1.a1', '360.cj1.a1'], 'contains': ['1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8790, -1, 8800, -1, 8512, -1, 7188, -1], 'generators': [3669120, 8023686], 'label': '2880.hl.720.z1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '720.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.z1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537010
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '720.ba1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ba1.a1', '240.bi1.a1', '360.m1.a1', '360.q1.a1', '360.bt1.a1', '360.cb1.a1', '360.cc1.a1', '360.ce1.a1', '360.cj1.a1'], 'contains': ['1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8997, -1, 9399, -1, 9053, -1, 7257, -1], 'generators': [8025256, 3669120], 'label': '2880.hl.720.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537011
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bb1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bb1.a1', '240.bj1.a1', '240.bn1.a1', '240.bp1.a1', '360.r1.a1', '360.bu1.a1', '360.ca1.a1', '360.cb1.a1', '360.cf1.a1', '360.cg1.a1', '360.ch1.a1'], 'contains': ['1440.c1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8329, -1, 8665, -1, 8353, -1, 7168, -1], 'generators': [3669120, 8025261], 'label': '2880.hl.720.bb1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537012
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '720.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bc1.a1', '240.bq1.a1', '360.b1.a1', '360.bx1.a1', '360.ck1.a1'], 'contains': ['1440.d1.a1', '1440.e1.a1', '1440.h1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5360, -1, 5326, -1, 4889, -1, 7647, -1], 'generators': [136, 5], 'label': '2880.hl.720.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '720.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537013
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bd1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bd1.a1', '240.br1.a1', '240.bu1.a1', '360.u1.a1', '360.br1.a1', '360.ck1.a1'], 'contains': ['1440.d1.a1', '1440.f1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4258, -1, 4544, -1, 4396, -1, 7380, -1], 'generators': [5, 3669840], 'label': '2880.hl.720.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537014
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.j1.a1', '6.s1.a1'], 'contains': ['24.p1.a1', '24.s1.a1', '24.z1.a1', '36.u1.a1', '60.t1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7590, -1, 6794, -1, 7364, -1, 7753, -1], 'generators': [23, 3669960, 8025136, 1463, 8025253, 50803200], 'label': '2880.hl.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.z1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183537015
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '720.be1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.be1.a1', '240.bs1.a1', '360.g1.a1', '360.bv1.a1', '360.ck1.a1'], 'contains': ['1440.d1.a1', '1440.g1.a1', '1440.i1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5427, -1, 5451, -1, 5123, -1, 7995, -1], 'generators': [5, 3669136], 'label': '2880.hl.720.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '720.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.be1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537016
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bf1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bf1.a1', '240.bt1.a1', '360.u1.a1', '360.bv1.a1', '360.bx1.a1'], 'contains': ['1440.d1.a1', '1440.j1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5253, -1, 5263, -1, 4911, -1, 7713, -1], 'generators': [5, 3669856], 'label': '2880.hl.720.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.bf1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537017
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '720.bg1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bg1.a1', '240.bv1.a1', '360.a1.a1', '360.x1.a1', '360.ck1.a1', '360.cl1.a1'], 'contains': ['1440.e1.a1', '1440.f1.a1', '1440.g1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5657, -1, 5771, -1, 5459, -1, 7669, -1], 'generators': [143, 3669143], 'label': '2880.hl.720.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '720.bg1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537018
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bh1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bh1.a1', '240.bw1.a1', '360.c1.a1', '360.h1.a1', '360.x1.a1'], 'contains': ['1440.e1.a1', '1440.g1.a1', '1440.j1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5606, -1, 5735, -1, 5225, -1, 6256, -1], 'generators': [127, 3669143], 'label': '2880.hl.720.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.j1.a1', 'old_label': '720.bh1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537019
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bi1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bi1.a1', '240.bx1.a1', '360.d1.a1', '360.bx1.a1', '360.ck1.a1'], 'contains': ['1440.e1.a1', '1440.i1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5184, -1, 5206, -1, 4742, -1, 7691, -1], 'generators': [136, 3669125], 'label': '2880.hl.720.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.bi1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537020
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bj1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bj1.a1', '240.by1.a1', '240.bz1.a1', '360.bb1.a1', '360.br1.a1', '360.ck1.a1'], 'contains': ['1440.f1.a1', '1440.h1.a1', '1440.i1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3989, -1, 4259, -1, 4418, -1, 7446, -1], 'generators': [3669125, 3669840], 'label': '2880.hl.720.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.bj1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537021
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bk1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bk1.a1', '240.ca1.a1', '360.i1.a1', '360.bv1.a1', '360.ck1.a1'], 'contains': ['1440.g1.a1', '1440.h1.a1', '1440.k1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4563, -1, 5051, -1, 4720, -1, 7973, -1], 'generators': [122, 3669143], 'label': '2880.hl.720.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.bk1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537022
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '720.bl1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '30.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bl1.a1', '240.cb1.a1', '360.o1.a1', '360.bw1.a1', '360.cl1.a1'], 'contains': ['1440.g1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6601, -1, 6781, -1, 7123, -1, 8161, -1], 'generators': [8023697, 3669127], 'label': '2880.hl.720.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '720.bl1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537023
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bm1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bm1.a1', '240.cc1.a1', '360.s1.a1', '360.bw1.a1', '360.cl1.a1'], 'contains': ['1440.g1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6626, -1, 6322, -1, 7080, -1, 8186, -1], 'generators': [8025253, 3669143], 'label': '2880.hl.720.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '720.bm1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537024
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '720.bn1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bn1.a1', '240.cd1.a1', '360.bb1.a1', '360.bv1.a1', '360.bx1.a1'], 'contains': ['1440.h1.a1', '1440.i1.a1', '1440.j1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5073, -1, 4577, -1, 4764, -1, 7735, -1], 'generators': [3669125, 3669856], 'label': '2880.hl.720.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.bn1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537025
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.j1.a1', '6.t1.a1'], 'contains': ['24.p1.a1', '24.t1.a1', '24.w1.a1', '24.cx1.a1', '24.cy1.a1', '36.v1.a1', '60.u1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8899, -1, 8874, -1, 7287, -1, 8252, -1], 'generators': [23, 3669960, 122, 1463, 8025141, 50803200], 'label': '2880.hl.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ba1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183537026
    {'ambient': '2880.hl', 'aut_centralizer_order': 1440, 'aut_label': '960.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '2.d1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '320.a1.a1', '480.a1.a1', '480.b1.a1', '480.d1.a1', '480.g1.a1', '480.i1.a1', '480.k1.a1', '480.l1.a1', '480.m1.a1', '480.p1.a1', '480.r1.a1', '480.s1.a1'], 'contains': ['2880.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5114, 4899, 4972, 4547, 4572, 4441, 7491, 5774], 'generators': [1440], 'label': '2880.hl.960.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '960.a1.a1', 'normal_contained_in': ['192.a1.a1', '240.a1.a1', '480.a1.a1'], 'normal_contains': ['2880.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '960.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': '2.1', 'quotient_action_kernel': '480.1189', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183537027
    {'ambient': '2880.hl', 'aut_centralizer_order': 360, 'aut_label': '960.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '240.b1.a1', '320.a1.a1', '480.c1.a1', '480.e1.a1', '480.h1.a1', '480.j1.a1', '480.n1.a1', '480.q1.a1', '480.t1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1918, -1, 1667, -1, 1194, -1, 870, -1], 'generators': [11], 'label': '2880.hl.960.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '960.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183537028
    {'ambient': '2880.hl', 'aut_centralizer_order': 180, 'aut_label': '960.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1440, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.a1', '240.q1.a1', '320.a1.a1', '480.f1.a1', '480.o1.a1', '480.u1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1955, -1, 2058, -1, 1238, -1, 1177, -1], 'generators': [1460], 'label': '2880.hl.960.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '960.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 183537029
    {'ambient': '2880.hl', 'aut_centralizer_order': 960, 'aut_label': '1440.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.b1.a1', '480.b1.a1', '720.a1.a1', '720.b1.a1', '720.c1.a1', '720.d1.a1', '720.e1.a1', '720.f1.a1', '720.g1.a1', '720.h1.a1', '720.i1.a1', '720.j1.a1', '720.k1.a1', '720.l1.a1', '720.m1.a1', '720.n1.a1', '720.o1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3213, -1, 2940, -1, 3183, -1, 3839, -1], 'generators': [7], 'label': '2880.hl.1440.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '720.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '1440.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537030
    {'ambient': '2880.hl', 'aut_centralizer_order': 960, 'aut_label': '1440.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.c1.a1', '480.a1.a1', '480.c1.a1', '720.b1.a1', '720.p1.a1', '720.q1.a1', '720.r1.a1', '720.s1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4223, -1, 4104, -1, 4400, -1, 7402, -1], 'generators': [120], 'label': '2880.hl.1440.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '480.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '1440.b1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537031
    {'ambient': '2880.hl', 'aut_centralizer_order': 576, 'aut_label': '1440.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '480.d1.a1', '480.e1.a1', '480.f1.a1', '720.c1.a1', '720.p1.a1', '720.t1.a1', '720.u1.a1', '720.v1.a1', '720.w1.a1', '720.x1.a1', '720.y1.a1', '720.z1.a1', '720.ba1.a1', '720.bb1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6554, -1, 6776, -1, 6517, -1, 7212, -1], 'generators': [3669120], 'label': '2880.hl.1440.c1.a1', 'mobius_quo': None, 'mobius_sub': -288, 'normal_closure': '288.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '1440.c1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537032
    {'ambient': '2880.hl', 'aut_centralizer_order': 480, 'aut_label': '1440.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.d1.a1', '480.g1.a1', '480.h1.a1', '720.d1.a1', '720.q1.a1', '720.t1.a1', '720.bc1.a1', '720.bd1.a1', '720.be1.a1', '720.bf1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5209, -1, 4990, -1, 4521, -1, 7511, -1], 'generators': [5], 'label': '2880.hl.1440.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '1440.d1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537033
    {'ambient': '2880.hl', 'aut_centralizer_order': 320, 'aut_label': '1440.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1.a1', '480.i1.a1', '720.b1.a1', '720.e1.a1', '720.u1.a1', '720.bc1.a1', '720.bg1.a1', '720.bh1.a1', '720.bi1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5501, -1, 5408, -1, 4844, -1, 7530, -1], 'generators': [127], 'label': '2880.hl.1440.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '1440.e1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537034
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '1440.f1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.f1.a1', '480.j1.a1', '480.k1.a1', '720.f1.a1', '720.p1.a1', '720.bd1.a1', '720.bg1.a1', '720.bj1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3968, -1, 4259, -1, 4420, -1, 7380, -1], 'generators': [3669840], 'label': '2880.hl.1440.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '1440.f1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537035
    {'ambient': '2880.hl', 'aut_centralizer_order': 192, 'aut_label': '1440.g1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.g1.a1', '480.l1.a1', '720.c1.a1', '720.g1.a1', '720.r1.a1', '720.be1.a1', '720.bg1.a1', '720.bh1.a1', '720.bk1.a1', '720.bl1.a1', '720.bm1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5649, -1, 5763, -1, 5449, -1, 7898, -1], 'generators': [3669143], 'label': '2880.hl.1440.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '1440.g1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537036
    {'ambient': '2880.hl', 'aut_centralizer_order': 2, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 6, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.i1.a1', '6.t1.a1'], 'contains': ['24.p1.a1', '24.v1.a1', '24.x1.a1', '36.w1.a1', '60.v1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6969, -1, 7395, -1, 7849, -1, 7875, -1], 'generators': [23, 3669960, 122, 1463, 8025133, 50803200], 'label': '2880.hl.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bb1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '480.1197'}
  • id: 183537037
    {'ambient': '2880.hl', 'aut_centralizer_order': 160, 'aut_label': '1440.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.h1.a1', '480.m1.a1', '480.n1.a1', '480.o1.a1', '720.h1.a1', '720.q1.a1', '720.v1.a1', '720.bc1.a1', '720.bj1.a1', '720.bk1.a1', '720.bn1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4295, -1, 4390, -1, 4479, -1, 7472, -1], 'generators': [122], 'label': '2880.hl.1440.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '1440.h1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537038
    {'ambient': '2880.hl', 'aut_centralizer_order': 96, 'aut_label': '1440.i1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '30.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.i1.a1', '480.p1.a1', '480.q1.a1', '720.i1.a1', '720.s1.a1', '720.t1.a1', '720.be1.a1', '720.bi1.a1', '720.bj1.a1', '720.bn1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5057, -1, 4560, -1, 4499, -1, 7549, -1], 'generators': [3669125], 'label': '2880.hl.1440.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '1440.i1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537039
    {'ambient': '2880.hl', 'aut_centralizer_order': 64, 'aut_label': '1440.j1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.j1.a1', '480.r1.a1', '720.f1.a1', '720.j1.a1', '720.r1.a1', '720.u1.a1', '720.bf1.a1', '720.bh1.a1', '720.bn1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5389, -1, 5304, -1, 4879, -1, 7598, -1], 'generators': [3669863], 'label': '2880.hl.1440.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '1440.j1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537040
    {'ambient': '2880.hl', 'aut_centralizer_order': 32, 'aut_label': '1440.k1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.k1.a1', '480.s1.a1', '480.t1.a1', '480.u1.a1', '720.k1.a1', '720.s1.a1', '720.v1.a1', '720.bd1.a1', '720.bf1.a1', '720.bi1.a1', '720.bk1.a1'], 'contains': ['2880.a1.a1'], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4570, -1, 4580, -1, 4460, -1, 7453, -1], 'generators': [3669842], 'label': '2880.hl.1440.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.k1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537041
    {'ambient': '2880.hl', 'aut_centralizer_order': None, 'aut_label': '2880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['576.a1.a1', '960.a1.a1', '960.b1.a1', '960.c1.a1', '1440.a1.a1', '1440.b1.a1', '1440.c1.a1', '1440.d1.a1', '1440.e1.a1', '1440.f1.a1', '1440.g1.a1', '1440.h1.a1', '1440.i1.a1', '1440.j1.a1', '1440.k1.a1'], 'contains': [], 'core': '2880.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4942, 4899, 4560, 4547, 4479, 4441, 7472, 5774], 'generators': [], 'label': '2880.hl.2880.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '2880.a1.a1', 'normal_contained_in': ['576.a1.a1', '720.a1.a1', '960.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '2880.a1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 183537042
    {'ambient': '2880.hl', 'aut_centralizer_order': 12, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 36, 'centralizer': '240.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.i1.a1', '6.p1.a1'], 'contains': ['24.q1.a1', '24.r1.a1', '24.v1.a1', '36.x1.a1', '60.w1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7331, -1, 7814, -1, 6352, -1, 7513, -1], 'generators': [3669960, 1456, 9, 8025138, 50803200, 16], 'label': '2880.hl.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bc1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 183537043
    {'ambient': '2880.hl', 'aut_centralizer_order': 4, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '240.195', 'aut_weyl_index': 12, 'centralizer': '720.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.g1.a1', '6.s1.a1'], 'contains': ['24.q1.a1', '24.u1.a1', '24.z1.a1', '36.y1.a1', '60.x1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7841, -1, 7287, -1, 6258, -1, 7425, -1], 'generators': [23, 3669960, 8025143, 1463, 8025253, 50803200], 'label': '2880.hl.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bd1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
  • id: 183537044
    {'ambient': '2880.hl', 'aut_centralizer_order': 6, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '160.236', 'aut_weyl_index': 18, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.j1.a1', '6.p1.a1'], 'contains': ['24.r1.a1', '24.s1.a1', '24.w1.a1', '36.z1.a1', '60.y1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9479, -1, 9010, -1, 7527, -1, 7043, -1], 'generators': [3669960, 1456, 9, 8025134, 50803200, 16], 'label': '2880.hl.12.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.be1.a1', 'projective_image': '2880.hl', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '160.236'}