Abstract group data - 21600.y

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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 120, 'aut_gen_orders': [4, 4, 12], 'aut_gens': [[39916800, 40222474, 79833600, 4837853248], [39916800, 1999832429, 43545600, 5396411675], [83462400, 4917738781, 43545600, 5316870785], [3628800, 5795614979, 79833600, 5396401591]], 'aut_group': '172800.a', 'aut_hash': 7801507312597102089, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 172800, 'aut_permdeg': 33, 'aut_perms': [3657296292490407935070963261553014754, 2033668924887698056843911433989188957, 5502086605957461885442744024900939508], 'aut_phi_ratio': 30.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 15, 2, 1], [2, 45, 2, 1], [2, 225, 1, 1], [2, 675, 1, 1], [3, 2, 1, 1], [3, 20, 2, 1], [3, 40, 2, 1], [3, 400, 1, 1], [3, 800, 1, 1], [5, 12, 4, 1], [5, 144, 4, 1], [6, 30, 2, 1], [6, 60, 2, 1], [6, 300, 2, 1], [6, 450, 1, 1], [6, 600, 2, 1], [6, 900, 2, 1], [6, 1200, 1, 1], [10, 36, 4, 1], [10, 180, 4, 1], [10, 432, 4, 1], [10, 540, 4, 1], [15, 24, 4, 1], [15, 240, 4, 1], [15, 288, 4, 1], [15, 480, 4, 1], [30, 360, 4, 1], [30, 720, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_5^2:D_6', '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': 120, 'autcentquo_group': '172800.a', 'autcentquo_hash': 7801507312597102089, 'autcentquo_nilpotent': False, 'autcentquo_order': 172800, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_5^2:D_6', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 15, 2], [2, 45, 2], [2, 225, 1], [2, 675, 1], [3, 2, 1], [3, 20, 2], [3, 40, 2], [3, 400, 1], [3, 800, 1], [5, 12, 4], [5, 144, 4], [6, 30, 2], [6, 60, 2], [6, 300, 2], [6, 450, 1], [6, 600, 2], [6, 900, 2], [6, 1200, 1], [10, 36, 4], [10, 180, 4], [10, 432, 4], [10, 540, 4], [15, 24, 4], [15, 240, 4], [15, 288, 4], [15, 480, 4], [30, 360, 4], [30, 720, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '21600.y', 'commutator_count': 1, 'commutator_label': '10800.u', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '60.5', '60.5'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 25, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['6.1', 1], ['60.5', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 15, 1, 2], [2, 45, 1, 2], [2, 225, 1, 1], [2, 675, 1, 1], [3, 2, 1, 1], [3, 20, 1, 2], [3, 40, 1, 2], [3, 400, 1, 1], [3, 800, 1, 1], [5, 12, 2, 2], [5, 144, 2, 2], [6, 30, 1, 2], [6, 60, 1, 2], [6, 300, 1, 2], [6, 450, 1, 1], [6, 600, 1, 2], [6, 900, 1, 2], [6, 1200, 1, 1], [10, 36, 2, 2], [10, 180, 2, 2], [10, 432, 2, 2], [10, 540, 2, 2], [15, 24, 2, 2], [15, 240, 2, 2], [15, 288, 2, 2], [15, 480, 2, 2], [30, 360, 2, 2], [30, 720, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 513, 'exponent': 30, 'exponents_of_order': [5, 3, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[18, 1, 4], [24, 1, 4], [30, 1, 4], [32, 1, 1], [40, 1, 2], [50, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '21600.y', 'hash': 6859003311102709662, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 2, 3, 10], 'inner_gens': [[39916800, 40222474, 43545600, 4917686848], [39916800, 40222474, 43545600, 5875402498], [83462400, 83768074, 79833600, 4874141248], [83462400, 5396735128, 43545600, 4837853248]], 'inner_hash': 6859003311102709662, 'inner_nilpotent': False, 'inner_order': 21600, 'inner_split': True, 'inner_tex': 'S_3\\times A_5^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 18, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 18, 'irrep_stats': [[1, 2], [2, 1], [3, 8], [4, 4], [5, 4], [6, 4], [8, 2], [9, 8], [10, 2], [12, 8], [15, 8], [16, 2], [18, 4], [20, 4], [24, 4], [25, 2], [30, 4], [32, 1], [40, 2], [50, 1]], 'label': '21600.y', 'linC_count': 16, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'S3*A5^2', 'ngens': 4, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 30, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 75, 'number_divisions': 51, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 424, 'number_subgroup_classes': 782, 'number_subgroups': 132786, 'old_label': None, 'order': 21600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1023], [3, 1322], [5, 624], [6, 5430], [10, 4752], [15, 4128], [30, 4320]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [250016, 5312978073], 'outer_gens': [[39916800, 5832184169, 79833600, 1963882470], [39916800, 4874178085, 79833600, 5316864329]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [5, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 4], [5, 4], [6, 4], [8, 2], [10, 2], [12, 2], [16, 2], [18, 4], [20, 4], [24, 4], [25, 2], [30, 4], [32, 1], [36, 2], [40, 2], [48, 2], [50, 1], [60, 2]], 'representations': {'Perm': {'d': 13, 'gens': [39916800, 40222474, 79833600, 4837853248]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times A_5^2', 'transitive_degree': 75, '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: 109256869
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 25, 'group_order': 21600, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109256880
    {'aut_label': '2A', 'centralizer': '3.a1.a1', 'counter': 2, 'group_counter': 25, 'group_order': 21600, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 83462400, 'size': 3}
  • id: 109256891
    {'aut_label': '2B', 'centralizer': '15.b1.a1', 'counter': 3, 'group_counter': 25, 'group_order': 21600, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 21744, 'size': 15}
  • id: 109256902
    {'aut_label': '2B', 'centralizer': '15.b1.b1', 'counter': 4, 'group_counter': 25, 'group_order': 21600, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 1959914881, 'size': 15}
  • id: 109256913
    {'aut_label': '2D', 'centralizer': '45.a1.b1', 'counter': 5, 'group_counter': 25, 'group_order': 21600, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 1999831682, 'size': 45}
  • id: 109256924
    {'aut_label': '2D', 'centralizer': '45.a1.a1', 'counter': 6, 'group_counter': 25, 'group_order': 21600, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 83484144, 'size': 45}
  • id: 109256935
    {'aut_label': '2F', 'centralizer': '225.c1.a1', 'counter': 7, 'group_counter': 25, 'group_order': 21600, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 1959930965, 'size': 225}
  • id: 109256942
    {'aut_label': '2G', 'centralizer': '675.a1.a1', 'counter': 8, 'group_counter': 25, 'group_order': 21600, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 2043394802, 'size': 675}
  • id: 109256943
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 9, 'group_counter': 25, 'group_order': 21600, 'label': '3A', 'order': 3, 'powers': [9, 1, 9], 'representative': 79833600, 'size': 2}
  • id: 109256870
    {'aut_label': '3B', 'centralizer': '20.a1.b1', 'counter': 10, 'group_counter': 25, 'group_order': 21600, 'label': '3B', 'order': 3, 'powers': [10, 1, 10], 'representative': 1440, 'size': 20}
  • id: 109256871
    {'aut_label': '3B', 'centralizer': '20.a1.a1', 'counter': 11, 'group_counter': 25, 'group_order': 21600, 'label': '3C', 'order': 3, 'powers': [11, 1, 11], 'representative': 247832, 'size': 20}
  • id: 109256872
    {'aut_label': '3D', 'centralizer': '40.a1.a1', 'counter': 12, 'group_counter': 25, 'group_order': 21600, 'label': '3D', 'order': 3, 'powers': [12, 1, 12], 'representative': 80081432, 'size': 40}
  • id: 109256873
    {'aut_label': '3D', 'centralizer': '40.a1.b1', 'counter': 13, 'group_counter': 25, 'group_order': 21600, 'label': '3E', 'order': 3, 'powers': [13, 1, 13], 'representative': 43565904, 'size': 40}
  • id: 109256874
    {'aut_label': '3F', 'centralizer': '400.a1.a1', 'counter': 14, 'group_counter': 25, 'group_order': 21600, 'label': '3F', 'order': 3, 'powers': [14, 1, 14], 'representative': 15988, 'size': 400}
  • id: 109256875
    {'aut_label': '3G', 'centralizer': '800.a1.a1', 'counter': 15, 'group_counter': 25, 'group_order': 21600, 'label': '3G', 'order': 3, 'powers': [15, 1, 15], 'representative': 5392807353, 'size': 800}
  • id: 109256876
    {'aut_label': '5A1', 'centralizer': '12.a1.a1', 'counter': 16, 'group_counter': 25, 'group_order': 21600, 'label': '5A1', 'order': 5, 'powers': [17, 17, 1], 'representative': 5792221740, 'size': 12}
  • id: 109256877
    {'aut_label': '5A1', 'centralizer': '12.a1.a1', 'counter': 17, 'group_counter': 25, 'group_order': 21600, 'label': '5A2', 'order': 5, 'powers': [16, 16, 1], 'representative': 5312931995, 'size': 12}
  • id: 109256878
    {'aut_label': '5A1', 'centralizer': '12.a1.b1', 'counter': 18, 'group_counter': 25, 'group_order': 21600, 'label': '5B1', 'order': 5, 'powers': [19, 19, 1], 'representative': 10224, 'size': 12}
  • id: 109256879
    {'aut_label': '5A1', 'centralizer': '12.a1.b1', 'counter': 19, 'group_counter': 25, 'group_order': 21600, 'label': '5B2', 'order': 5, 'powers': [18, 18, 1], 'representative': 16824, 'size': 12}
  • id: 109256881
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 20, 'group_counter': 25, 'group_order': 21600, 'label': '5C1', 'order': 5, 'powers': [21, 21, 1], 'representative': 5312937895, 'size': 144}
  • id: 109256882
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 21, 'group_counter': 25, 'group_order': 21600, 'label': '5C2', 'order': 5, 'powers': [20, 20, 1], 'representative': 5792273821, 'size': 144}
  • id: 109256883
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 22, 'group_counter': 25, 'group_order': 21600, 'label': '5D1', 'order': 5, 'powers': [23, 23, 1], 'representative': 4834265369, 'size': 144}
  • id: 109256884
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 23, 'group_counter': 25, 'group_order': 21600, 'label': '5D2', 'order': 5, 'powers': [22, 22, 1], 'representative': 5312949415, 'size': 144}
  • id: 109256885
    {'aut_label': '6A', 'centralizer': '30.e1.b1', 'counter': 24, 'group_counter': 25, 'group_order': 21600, 'label': '6A', 'order': 6, 'powers': [9, 4, 24], 'representative': 2003460481, 'size': 30}
  • id: 109256886
    {'aut_label': '6A', 'centralizer': '30.e1.a1', 'counter': 25, 'group_counter': 25, 'group_order': 21600, 'label': '6B', 'order': 6, 'powers': [9, 3, 25], 'representative': 79838760, 'size': 30}
  • id: 109256887
    {'aut_label': '6C', 'centralizer': '60.b1.b1', 'counter': 26, 'group_counter': 25, 'group_order': 21600, 'label': '6C', 'order': 6, 'powers': [10, 2, 26], 'representative': 83469000, 'size': 60}
  • id: 109256888
    {'aut_label': '6C', 'centralizer': '60.b1.a1', 'counter': 27, 'group_counter': 25, 'group_order': 21600, 'label': '6D', 'order': 6, 'powers': [11, 2, 27], 'representative': 5316601113, 'size': 60}
  • id: 109256889
    {'aut_label': '6E', 'centralizer': '300.d1.b1', 'counter': 28, 'group_counter': 25, 'group_order': 21600, 'label': '6E', 'order': 6, 'powers': [10, 4, 28], 'representative': 5792222727, 'size': 300}
  • id: 109256890
    {'aut_label': '6E', 'centralizer': '300.d1.a1', 'counter': 29, 'group_counter': 25, 'group_order': 21600, 'label': '6F', 'order': 6, 'powers': [11, 3, 29], 'representative': 253139, 'size': 300}
  • id: 109256892
    {'aut_label': '6G', 'centralizer': '450.h1.a1', 'counter': 30, 'group_counter': 25, 'group_order': 21600, 'label': '6G', 'order': 6, 'powers': [9, 7, 30], 'representative': 2003476565, 'size': 450}
  • id: 109256893
    {'aut_label': '6H', 'centralizer': '600.n1.a1', 'counter': 31, 'group_counter': 25, 'group_order': 21600, 'label': '6H', 'order': 6, 'powers': [12, 3, 31], 'representative': 43855494, 'size': 600}
  • id: 109256894
    {'aut_label': '6H', 'centralizer': '600.n1.b1', 'counter': 32, 'group_counter': 25, 'group_order': 21600, 'label': '6I', 'order': 6, 'powers': [13, 4, 32], 'representative': 2039755825, 'size': 600}
  • id: 109256895
    {'aut_label': '6J', 'centralizer': '900.b1.b1', 'counter': 33, 'group_counter': 25, 'group_order': 21600, 'label': '6J', 'order': 6, 'powers': [10, 5, 33], 'representative': 1999832522, 'size': 900}
  • id: 109256896
    {'aut_label': '6J', 'centralizer': '900.b1.a1', 'counter': 34, 'group_counter': 25, 'group_order': 21600, 'label': '6K', 'order': 6, 'powers': [11, 6, 34], 'representative': 83772294, 'size': 900}
  • id: 109256897
    {'aut_label': '6L', 'centralizer': '1200.a1.a1', 'counter': 35, 'group_counter': 25, 'group_order': 21600, 'label': '6L', 'order': 6, 'powers': [14, 2, 35], 'representative': 3649803, 'size': 1200}
  • id: 109256898
    {'aut_label': '10A1', 'centralizer': '36.a1.a1', 'counter': 36, 'group_counter': 25, 'group_order': 21600, 'label': '10A1', 'order': 10, 'powers': [16, 37, 2], 'representative': 2043705754, 'size': 36}
  • id: 109256899
    {'aut_label': '10A1', 'centralizer': '36.a1.a1', 'counter': 37, 'group_counter': 25, 'group_order': 21600, 'label': '10A3', 'order': 10, 'powers': [17, 36, 2], 'representative': 4917680943, 'size': 36}
  • id: 109256900
    {'aut_label': '10A1', 'centralizer': '36.a1.b1', 'counter': 38, 'group_counter': 25, 'group_order': 21600, 'label': '10B1', 'order': 10, 'powers': [19, 39, 2], 'representative': 3650400, 'size': 36}
  • id: 109256901
    {'aut_label': '10A1', 'centralizer': '36.a1.b1', 'counter': 39, 'group_counter': 25, 'group_order': 21600, 'label': '10B3', 'order': 10, 'powers': [18, 38, 2], 'representative': 3636240, 'size': 36}
  • id: 109256903
    {'aut_label': '10C1', 'centralizer': '180.f1.b1', 'counter': 40, 'group_counter': 25, 'group_order': 21600, 'label': '10C1', 'order': 10, 'powers': [18, 41, 4], 'representative': 1959937321, 'size': 180}
  • id: 109256904
    {'aut_label': '10C1', 'centralizer': '180.f1.b1', 'counter': 41, 'group_counter': 25, 'group_order': 21600, 'label': '10C3', 'order': 10, 'powers': [19, 40, 4], 'representative': 1959922081, 'size': 180}
  • id: 109256905
    {'aut_label': '10C1', 'centralizer': '180.f1.a1', 'counter': 42, 'group_counter': 25, 'group_order': 21600, 'label': '10D1', 'order': 10, 'powers': [17, 43, 3], 'representative': 1960208195, 'size': 180}
  • id: 109256906
    {'aut_label': '10C1', 'centralizer': '180.f1.a1', 'counter': 43, 'group_counter': 25, 'group_order': 21600, 'label': '10D3', 'order': 10, 'powers': [16, 42, 3], 'representative': 4834264022, 'size': 180}
  • id: 109256907
    {'aut_label': '10E1', 'centralizer': '432.a1.a1', 'counter': 44, 'group_counter': 25, 'group_order': 21600, 'label': '10E1', 'order': 10, 'powers': [20, 45, 2], 'representative': 2043715978, 'size': 432}
  • id: 109256908
    {'aut_label': '10E1', 'centralizer': '432.a1.a1', 'counter': 45, 'group_counter': 25, 'group_order': 21600, 'label': '10E3', 'order': 10, 'powers': [21, 44, 2], 'representative': 4917703383, 'size': 432}
  • id: 109256909
    {'aut_label': '10E1', 'centralizer': '432.a1.a1', 'counter': 46, 'group_counter': 25, 'group_order': 21600, 'label': '10F1', 'order': 10, 'powers': [22, 47, 2], 'representative': 5396401591, 'size': 432}
  • id: 109256910
    {'aut_label': '10E1', 'centralizer': '432.a1.a1', 'counter': 47, 'group_counter': 25, 'group_order': 21600, 'label': '10F3', 'order': 10, 'powers': [23, 46, 2], 'representative': 4917738089, 'size': 432}
  • id: 109256911
    {'aut_label': '10G1', 'centralizer': '540.b1.a1', 'counter': 48, 'group_counter': 25, 'group_order': 21600, 'label': '10G1', 'order': 10, 'powers': [17, 49, 6], 'representative': 5396411071, 'size': 540}
  • id: 109256912
    {'aut_label': '10G1', 'centralizer': '540.b1.a1', 'counter': 49, 'group_counter': 25, 'group_order': 21600, 'label': '10G3', 'order': 10, 'powers': [16, 48, 6], 'representative': 4917737945, 'size': 540}
  • id: 109256914
    {'aut_label': '10G1', 'centralizer': '540.b1.b1', 'counter': 50, 'group_counter': 25, 'group_order': 21600, 'label': '10H1', 'order': 10, 'powers': [18, 51, 5], 'representative': 4874191045, 'size': 540}
  • id: 109256915
    {'aut_label': '10G1', 'centralizer': '540.b1.b1', 'counter': 51, 'group_counter': 25, 'group_order': 21600, 'label': '10H3', 'order': 10, 'powers': [19, 50, 5], 'representative': 4874197261, 'size': 540}
  • id: 109256916
    {'aut_label': '15A1', 'centralizer': '24.a1.b1', 'counter': 52, 'group_counter': 25, 'group_order': 21600, 'label': '15A1', 'order': 15, 'powers': [53, 18, 9], 'representative': 43562424, 'size': 24}
  • id: 109256917
    {'aut_label': '15A1', 'centralizer': '24.a1.b1', 'counter': 53, 'group_counter': 25, 'group_order': 21600, 'label': '15A2', 'order': 15, 'powers': [52, 19, 9], 'representative': 79840800, 'size': 24}
  • id: 109256918
    {'aut_label': '15A1', 'centralizer': '24.a1.a1', 'counter': 54, 'group_counter': 25, 'group_order': 21600, 'label': '15B1', 'order': 15, 'powers': [55, 17, 9], 'representative': 5871767194, 'size': 24}
  • id: 109256919
    {'aut_label': '15A1', 'centralizer': '24.a1.a1', 'counter': 55, 'group_counter': 25, 'group_order': 21600, 'label': '15B2', 'order': 15, 'powers': [54, 16, 9], 'representative': 4877804462, 'size': 24}
  • id: 109256920
    {'aut_label': '15C1', 'centralizer': '240.a1.a1', 'counter': 56, 'group_counter': 25, 'group_order': 21600, 'label': '15C1', 'order': 15, 'powers': [57, 16, 10], 'representative': 5312938595, 'size': 240}
  • id: 109256921
    {'aut_label': '15C1', 'centralizer': '240.a1.a1', 'counter': 57, 'group_counter': 25, 'group_order': 21600, 'label': '15C2', 'order': 15, 'powers': [56, 17, 10], 'representative': 4834233783, 'size': 240}
  • id: 109256922
    {'aut_label': '15C1', 'centralizer': '240.a1.b1', 'counter': 58, 'group_counter': 25, 'group_order': 21600, 'label': '15D1', 'order': 15, 'powers': [59, 19, 11], 'representative': 5312983977, 'size': 240}
  • id: 109256923
    {'aut_label': '15C1', 'centralizer': '240.a1.b1', 'counter': 59, 'group_counter': 25, 'group_order': 21600, 'label': '15D2', 'order': 15, 'powers': [58, 18, 11], 'representative': 5791981352, 'size': 240}
  • id: 109256925
    {'aut_label': '15E1', 'centralizer': '288.a1.a1', 'counter': 60, 'group_counter': 25, 'group_order': 21600, 'label': '15E1', 'order': 15, 'powers': [61, 20, 9], 'representative': 5872107421, 'size': 288}
  • id: 109256926
    {'aut_label': '15E1', 'centralizer': '288.a1.a1', 'counter': 61, 'group_counter': 25, 'group_order': 21600, 'label': '15E2', 'order': 15, 'powers': [60, 21, 9], 'representative': 2003728474, 'size': 288}
  • id: 109256927
    {'aut_label': '15E1', 'centralizer': '288.a1.a1', 'counter': 62, 'group_counter': 25, 'group_order': 21600, 'label': '15F1', 'order': 15, 'powers': [63, 22, 9], 'representative': 5356495015, 'size': 288}
  • id: 109256928
    {'aut_label': '15E1', 'centralizer': '288.a1.a1', 'counter': 63, 'group_counter': 25, 'group_order': 21600, 'label': '15F2', 'order': 15, 'powers': [62, 23, 9], 'representative': 5872105981, 'size': 288}
  • id: 109256929
    {'aut_label': '15G1', 'centralizer': '480.a1.b1', 'counter': 64, 'group_counter': 25, 'group_order': 21600, 'label': '15G1', 'order': 15, 'powers': [65, 18, 12], 'representative': 5835496017, 'size': 480}
  • id: 109256930
    {'aut_label': '15G1', 'centralizer': '480.a1.b1', 'counter': 65, 'group_counter': 25, 'group_order': 21600, 'label': '15G2', 'order': 15, 'powers': [64, 19, 12], 'representative': 2040084153, 'size': 480}
  • id: 109256931
    {'aut_label': '15G1', 'centralizer': '480.a1.a1', 'counter': 66, 'group_counter': 25, 'group_order': 21600, 'label': '15H1', 'order': 15, 'powers': [67, 16, 13], 'representative': 2040051871, 'size': 480}
  • id: 109256932
    {'aut_label': '15G1', 'centralizer': '480.a1.a1', 'counter': 67, 'group_counter': 25, 'group_order': 21600, 'label': '15H2', 'order': 15, 'powers': [66, 17, 13], 'representative': 5356812663, 'size': 480}
  • id: 109256933
    {'aut_label': '30A1', 'centralizer': '360.n1.b1', 'counter': 68, 'group_counter': 25, 'group_order': 21600, 'label': '30A1', 'order': 30, 'powers': [52, 40, 24], 'representative': 2039758705, 'size': 360}
  • id: 109256934
    {'aut_label': '30A1', 'centralizer': '360.n1.b1', 'counter': 69, 'group_counter': 25, 'group_order': 21600, 'label': '30A7', 'order': 30, 'powers': [53, 41, 24], 'representative': 2039765305, 'size': 360}
  • id: 109256936
    {'aut_label': '30A1', 'centralizer': '360.n1.a1', 'counter': 70, 'group_counter': 25, 'group_order': 21600, 'label': '30B1', 'order': 30, 'powers': [54, 42, 25], 'representative': 5356770901, 'size': 360}
  • id: 109256937
    {'aut_label': '30A1', 'centralizer': '360.n1.a1', 'counter': 71, 'group_counter': 25, 'group_order': 21600, 'label': '30B7', 'order': 30, 'powers': [55, 43, 25], 'representative': 5835484354, 'size': 360}
  • id: 109256938
    {'aut_label': '30C1', 'centralizer': '720.a1.a1', 'counter': 72, 'group_counter': 25, 'group_order': 21600, 'label': '30C1', 'order': 30, 'powers': [56, 36, 26], 'representative': 5875699380, 'size': 720}
  • id: 109256939
    {'aut_label': '30C1', 'centralizer': '720.a1.a1', 'counter': 73, 'group_counter': 25, 'group_order': 21600, 'label': '30C7', 'order': 30, 'powers': [57, 37, 26], 'representative': 5396409635, 'size': 720}
  • id: 109256940
    {'aut_label': '30C1', 'centralizer': '720.a1.b1', 'counter': 74, 'group_counter': 25, 'group_order': 21600, 'label': '30D1', 'order': 30, 'powers': [58, 38, 27], 'representative': 5795618096, 'size': 720}
  • id: 109256941
    {'aut_label': '30C1', 'centralizer': '720.a1.b1', 'counter': 75, 'group_counter': 25, 'group_order': 21600, 'label': '30D7', 'order': 30, 'powers': [59, 39, 27], 'representative': 5795614376, 'size': 720}
• 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: 4201514
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.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: 4201525
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.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: 4201536
    {'cdim': 2, 'counter': 3, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 0, 0, 2, 0, -1, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201563
    {'cdim': 4, 'counter': 8, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.4a', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 0, 0, 0, 4, 1, 4, 4, 1, 1, 1, 4, 4, -1, -1, -1, -1, -1, -1, 4, 0, 1, 4, 1, 0, 0, 0, 1, 1, 0, 1, 4, 4, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, -1, 0, -1, -1, -1, 4, 4, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4201564
    {'cdim': 4, 'counter': 9, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.4b', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 4, 0, 0, 4, 4, 1, 1, 4, 1, 1, -1, -1, 4, 4, -1, -1, -1, -1, 0, 4, 4, 1, 0, 1, 0, 1, 0, 0, 1, 1, -1, -1, 4, 4, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, -1, 0, 4, 4, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4201515
    {'cdim': 4, 'counter': 10, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.4c', 'multiplicity': 1, 'nt': [10, 11], 'qdim': 4, 'qvalues': [4, -4, 0, 4, -4, 0, 0, 0, 4, 1, 4, 4, 1, 1, 1, 4, 4, -1, -1, -1, -1, -1, -1, 4, 0, -1, -4, 1, 0, 0, 0, 1, -1, 0, -1, -4, -4, 1, 1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, -1, -1, 4, 4, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4201516
    {'cdim': 4, 'counter': 11, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.4d', 'multiplicity': 1, 'nt': [10, 11], 'qdim': 4, 'qvalues': [4, -4, 4, 0, 0, -4, 0, 0, 4, 4, 1, 1, 4, 1, 1, -1, -1, 4, 4, -1, -1, -1, -1, 0, 4, -4, -1, 0, 1, 0, 1, 0, 0, -1, -1, 1, 1, -4, -4, 0, 0, -1, -1, 1, 1, 1, 1, 1, 0, 1, 0, 4, 4, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4201517
    {'cdim': 5, 'counter': 12, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.5a', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 1, 5, 5, 1, 1, 1, 5, -1, 5, 5, -1, -1, -1, 5, 5, 0, 0, 0, 0, 0, 0, 5, 1, -1, 5, -1, 1, 1, 1, -1, -1, 1, -1, 5, 5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 5, 5, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4201518
    {'cdim': 5, 'counter': 13, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.5b', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 5, 1, 1, 5, 1, 1, 5, 5, -1, -1, 5, -1, -1, 0, 0, 5, 5, 0, 0, 0, 0, 1, 5, 5, -1, 1, -1, 1, -1, 1, 1, -1, -1, 0, 0, 5, 5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 5, 5, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4201519
    {'cdim': 5, 'counter': 14, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.5c', 'multiplicity': 1, 'nt': [12, 75], 'qdim': 5, 'qvalues': [5, -5, 1, 5, -5, -1, 1, -1, 5, -1, 5, 5, -1, -1, -1, 5, 5, 0, 0, 0, 0, 0, 0, 5, 1, 1, -5, -1, 1, 1, 1, -1, 1, -1, 1, -5, -5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 5, 5, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4201520
    {'cdim': 5, 'counter': 15, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.5d', 'multiplicity': 1, 'nt': [12, 75], 'qdim': 5, 'qvalues': [5, -5, 5, 1, -1, -5, 1, -1, 5, 5, -1, -1, 5, -1, -1, 0, 0, 5, 5, 0, 0, 0, 0, 1, 5, -5, 1, 1, -1, 1, -1, 1, -1, 1, 1, 0, 0, -5, -5, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 5, 5, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4201547
    {'cdim': 3, 'counter': 4, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.3a', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, -2, 6, 6, -2, -2, -2, 6, 0, 6, 6, 0, 0, 0, 6, 6, 1, 1, 1, 1, 1, 1, 6, -2, 0, 6, 0, -2, -2, -2, 0, 0, -2, 0, 6, 6, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 6, 6, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, -2, -2, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4201558
    {'cdim': 3, 'counter': 5, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.3b', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, 6, -2, -2, 6, -2, -2, 6, 6, 0, 0, 6, 0, 0, 1, 1, 6, 6, 1, 1, 1, 1, -2, 6, 6, 0, -2, 0, -2, 0, -2, -2, 0, 0, 1, 1, 6, 6, -2, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, 6, 6, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4201561
    {'cdim': 3, 'counter': 6, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.3c', 'multiplicity': 2, 'nt': [12, 76], 'qdim': 6, 'qvalues': [6, -6, -2, 6, -6, 2, -2, 2, 6, 0, 6, 6, 0, 0, 0, 6, 6, 1, 1, 1, 1, 1, 1, 6, -2, 0, -6, 0, -2, -2, -2, 0, 0, 2, 0, -6, -6, -1, -1, 1, 1, -2, -2, -1, -1, -1, -1, 2, -1, 2, -1, 1, 1, 6, 6, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, -2, -2, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4201562
    {'cdim': 3, 'counter': 7, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.3d', 'multiplicity': 2, 'nt': [12, 76], 'qdim': 6, 'qvalues': [6, -6, 6, -2, 2, -6, -2, 2, 6, 6, 0, 0, 6, 0, 0, 1, 1, 6, 6, 1, 1, 1, 1, -2, 6, -6, 0, -2, 0, -2, 0, -2, 2, 0, 0, -1, -1, -6, -6, -2, -2, 1, 1, -1, -1, -1, -1, -1, 2, -1, 2, 6, 6, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, -2, -2, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4201523
    {'cdim': 8, 'counter': 18, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.8a', 'multiplicity': 1, 'nt': [15, 23], 'qdim': 8, 'qvalues': [8, 0, 0, 8, 0, 0, 0, 0, -4, 2, 8, -4, -1, 2, -1, 8, 8, -2, -2, -2, -2, -2, -2, -4, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -4, -4, 2, -2, 2, -2, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201524
    {'cdim': 8, 'counter': 19, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.8b', 'multiplicity': 1, 'nt': [15, 23], 'qdim': 8, 'qvalues': [8, 0, 8, 0, 0, 0, 0, 0, -4, 8, 2, -1, -4, 2, -1, -2, -2, 8, 8, -2, -2, -2, -2, 0, -4, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 1, 1, -2, 2, -2, 2, 1, 1, 1, 1, -1, -1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201530
    {'cdim': 10, 'counter': 24, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.10a', 'multiplicity': 1, 'nt': [18, 145], 'qdim': 10, 'qvalues': [10, 0, 2, 10, 0, 0, 2, 0, -5, -2, 10, -5, 1, -2, 1, 10, 10, 0, 0, 0, 0, 0, 0, -5, -1, 0, 0, -2, 2, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201531
    {'cdim': 10, 'counter': 25, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.10b', 'multiplicity': 1, 'nt': [18, 145], 'qdim': 10, 'qvalues': [10, 0, 10, 2, 0, 0, 2, 0, -5, 10, -2, 1, -5, -2, 1, 0, 0, 10, 10, 0, 0, 0, 0, -1, -5, 0, 0, 2, -2, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201521
    {'cdim': 6, 'counter': 16, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.6a', 'multiplicity': 2, 'nt': [36, 551], 'qdim': 12, 'qvalues': [12, 0, -4, 12, 0, 0, -4, 0, -6, 0, 12, -6, 0, 0, 0, 12, 12, 2, 2, 2, 2, 2, 2, -6, 2, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -6, -6, 0, 2, 0, 2, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201522
    {'cdim': 6, 'counter': 17, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.6b', 'multiplicity': 2, 'nt': [36, 551], 'qdim': 12, 'qvalues': [12, 0, 12, -4, 0, 0, -4, 0, -6, 12, 0, 0, -6, 0, 0, 2, 2, 12, 12, 2, 2, 2, 2, 2, -6, 0, 0, -4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -1, -1, 2, 0, 2, 0, -1, -1, -1, -1, 0, 0, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201541
    {'cdim': 16, 'counter': 34, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.16a', 'multiplicity': 1, 'nt': [25, 77], 'qdim': 16, 'qvalues': [16, 16, 0, 0, 0, 0, 0, 0, 16, 4, 4, 4, 4, 1, 1, -4, -4, -4, -4, 1, 1, 1, 1, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 1, -4, -4, -4, -4, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -4, -4, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4201542
    {'cdim': 16, 'counter': 35, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.16b', 'multiplicity': 1, 'nt': [50, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 16, 4, 4, 4, 4, 1, 1, -4, -4, -4, -4, 1, 1, 1, 1, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, -1, 4, 4, 4, 4, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -4, -4, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4201526
    {'cdim': 9, 'counter': 20, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.9a', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 18, -6, -6, -6, -6, 2, 2, 18, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -2, 3, -2, 3, -6, -6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, -2, -2, 3, 3, -1, -1, -1, -1, 3, 3, 3, 3, 0, 0, 0, 0, 3, 3, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201527
    {'cdim': 9, 'counter': 21, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.9b', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 18, -6, -6, -6, -6, 2, 2, 18, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, -2, 3, -2, -6, -6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, 3, 3, -2, -2, -1, -1, -1, -1, 3, 3, 3, 3, 0, 0, 0, 0, -2, -2, 3, 3, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201528
    {'cdim': 9, 'counter': 22, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.9c', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 18, 'qvalues': [18, -18, -6, -6, 6, 6, 2, -2, 18, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -2, 3, -2, 3, -6, -6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -3, -3, -3, -3, -1, -1, -1, -1, 2, 2, -3, -3, 1, 1, 1, 1, 3, 3, 3, 3, 0, 0, 0, 0, 3, 3, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201529
    {'cdim': 9, 'counter': 23, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.9d', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 18, 'qvalues': [18, -18, -6, -6, 6, 6, 2, -2, 18, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, -2, 3, -2, -6, -6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -3, -3, -3, -3, -1, -1, -1, -1, -3, -3, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3, 0, 0, 0, 0, -2, -2, 3, 3, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201545
    {'cdim': 20, 'counter': 38, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.20a', 'multiplicity': 1, 'nt': [30, 472], 'qdim': 20, 'qvalues': [20, 20, 0, 4, 4, 0, 0, 0, 20, 5, -4, -4, 5, -1, -1, 0, 0, -5, -5, 0, 0, 0, 0, 4, 0, 5, -4, 1, 0, 0, 0, 1, 1, 0, -1, 0, 0, -5, -5, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -5, -5, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4201546
    {'cdim': 20, 'counter': 39, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.20b', 'multiplicity': 1, 'nt': [30, 472], 'qdim': 20, 'qvalues': [20, 20, 4, 0, 0, 4, 0, 0, 20, -4, 5, 5, -4, -1, -1, -5, -5, 0, 0, 0, 0, 0, 0, 0, 4, -4, 5, 0, 1, 0, 1, 0, 0, 1, -1, -5, -5, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -5, -5, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4201548
    {'cdim': 20, 'counter': 40, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.20c', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 20, 'qvalues': [20, -20, 0, 4, -4, 0, 0, 0, 20, 5, -4, -4, 5, -1, -1, 0, 0, -5, -5, 0, 0, 0, 0, 4, 0, -5, 4, 1, 0, 0, 0, 1, -1, 0, 1, 0, 0, 5, 5, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -5, -5, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4201549
    {'cdim': 20, 'counter': 41, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.20d', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 20, 'qvalues': [20, -20, 4, 0, 0, -4, 0, 0, 20, -4, 5, 5, -4, -1, -1, -5, -5, 0, 0, 0, 0, 0, 0, 0, 4, 4, -5, 0, 1, 0, 1, 0, 0, -1, 1, 5, 5, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -5, -5, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4201532
    {'cdim': 12, 'counter': 26, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.12a', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, -24, -8, 0, 0, 8, 0, 0, 24, 0, 6, 6, 0, 0, 0, -6, -6, 4, 4, -1, -1, -1, -1, 0, -8, 0, -6, 0, -2, 0, -2, 0, 0, 2, 0, 6, 6, -4, -4, 0, 0, 2, 2, 1, 1, 1, 1, -2, 0, -2, 0, 4, 4, -6, -6, 0, 1, 0, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4201533
    {'cdim': 12, 'counter': 27, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.12b', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, -24, 0, -8, 8, 0, 0, 0, 24, 6, 0, 0, 6, 0, 0, 4, 4, -6, -6, -1, -1, -1, -1, -8, 0, -6, 0, -2, 0, 0, 0, -2, 2, 0, 0, -4, -4, 6, 6, 2, 2, 0, 0, 1, 1, 1, 1, 0, -2, 0, -2, -6, -6, 4, 4, 1, 0, 1, 0, -1, -1, -1, -1, 0, 0, 1, 1, 2, 2, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4201534
    {'cdim': 12, 'counter': 28, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.12c', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, 24, -8, 0, 0, -8, 0, 0, 24, 0, 6, 6, 0, 0, 0, -6, -6, 4, 4, -1, -1, -1, -1, 0, -8, 0, 6, 0, -2, 0, -2, 0, 0, -2, 0, -6, -6, 4, 4, 0, 0, 2, 2, -1, -1, -1, -1, 2, 0, 2, 0, 4, 4, -6, -6, 0, 1, 0, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4201535
    {'cdim': 12, 'counter': 29, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.12d', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, 24, 0, -8, -8, 0, 0, 0, 24, 6, 0, 0, 6, 0, 0, 4, 4, -6, -6, -1, -1, -1, -1, -8, 0, 6, 0, -2, 0, 0, 0, -2, -2, 0, 0, 4, 4, -6, -6, 2, 2, 0, 0, -1, -1, -1, -1, 0, 2, 0, 2, -6, -6, 4, 4, 1, 0, 1, 0, -1, -1, -1, -1, 0, 0, 1, 1, 2, 2, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4201552
    {'cdim': 25, 'counter': 44, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.25a', 'multiplicity': 1, 'nt': [36, 4580], 'qdim': 25, 'qvalues': [25, 25, 5, 5, 5, 5, 1, 1, 25, -5, -5, -5, -5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, -5, -5, -1, -1, 1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201553
    {'cdim': 25, 'counter': 45, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.25b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 25, 'qvalues': [25, -25, 5, 5, -5, -5, 1, -1, 25, -5, -5, -5, -5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, -1, -1, 1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201537
    {'cdim': 15, 'counter': 30, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.15a', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 30, 'qvalues': [30, -30, -10, 6, -6, 10, -2, 2, 30, 0, -6, -6, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 6, -10, 0, 6, 0, 2, -2, 2, 0, 0, -2, 0, 0, 0, -5, -5, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 5, 5, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4201538
    {'cdim': 15, 'counter': 31, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.15b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 30, 'qvalues': [30, -30, 6, -10, 10, -6, -2, 2, 30, -6, 0, 0, -6, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, -10, 6, 6, 0, 2, 0, -2, 0, 2, -2, 0, 0, -5, -5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 5, 5, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4201539
    {'cdim': 15, 'counter': 32, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.15c', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 30, 'qvalues': [30, 30, -10, 6, 6, -10, -2, -2, 30, 0, -6, -6, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 6, -10, 0, -6, 0, 2, -2, 2, 0, 0, 2, 0, 0, 0, 5, 5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 5, 5, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4201540
    {'cdim': 15, 'counter': 33, 'faithful': False, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.15d', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 30, 'qvalues': [30, 30, 6, -10, -10, 6, -2, -2, 30, -6, 0, 0, -6, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, -10, 6, -6, 0, 2, 0, -2, 0, 2, 2, 0, 0, 5, 5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 5, 5, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4201556
    {'cdim': 32, 'counter': 48, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.32a', 'multiplicity': 1, 'nt': [75, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 0, 0, 0, 0, 0, -16, 8, 8, -4, -4, 2, -1, -8, -8, -8, -8, 2, 2, 2, 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, 4, 4, 4, 4, -2, -2, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201543
    {'cdim': 18, 'counter': 36, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.18a', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 36, 'qvalues': [36, 0, -12, -12, 0, 0, 4, 0, -18, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, -4, 6, -4, 6, 6, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, -3, -3, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201544
    {'cdim': 18, 'counter': 37, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.18b', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 36, 'qvalues': [36, 0, -12, -12, 0, 0, 4, 0, -18, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, -4, 6, -4, 6, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 2, 2, -3, -3, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201557
    {'cdim': 40, 'counter': 49, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.40a', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 40, 'qvalues': [40, 0, 0, 8, 0, 0, 0, 0, -20, 10, -8, 4, -5, -2, 1, 0, 0, -10, -10, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201559
    {'cdim': 40, 'counter': 50, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.40b', 'multiplicity': 1, 'nt': [90, 0], 'qdim': 40, 'qvalues': [40, 0, 8, 0, 0, 0, 0, 0, -20, -8, 10, -5, 4, -2, 1, -10, -10, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201550
    {'cdim': 24, 'counter': 42, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.24a', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 48, 'qvalues': [48, 0, -16, 0, 0, 0, 0, 0, -24, 0, 12, -6, 0, 0, 0, -12, -12, 8, 8, -2, -2, -2, -2, 0, 8, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 6, 6, 0, 2, 0, 2, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201551
    {'cdim': 24, 'counter': 43, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.24b', 'multiplicity': 2, 'nt': [180, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -16, 0, 0, 0, 0, -24, 12, 0, 0, -6, 0, 0, 8, 8, -12, -12, -2, -2, -2, -2, 8, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -4, -4, 2, 0, 2, 0, 1, 1, 1, 1, 0, 0, -1, -1, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201560
    {'cdim': 50, 'counter': 51, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.50a', 'multiplicity': 1, 'nt': [108, 0], 'qdim': 50, 'qvalues': [50, 0, 10, 10, 0, 0, 2, 0, -25, -10, -10, 5, 5, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, 0, 0, -2, -2, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201554
    {'cdim': 30, 'counter': 46, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.30a', 'multiplicity': 2, 'nt': [216, 0], 'qdim': 60, 'qvalues': [60, 0, -20, 12, 0, 0, -4, 0, -30, 0, -12, 6, 0, 0, 0, 0, 0, 10, 10, 0, 0, 0, 0, -6, 10, 0, 0, 0, 4, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4201555
    {'cdim': 30, 'counter': 47, 'faithful': True, 'group': '21600.y', 'group_order': 21600, 'image': None, 'label': '21600.y.30b', 'multiplicity': 2, 'nt': [216, 0], 'qdim': 60, 'qvalues': [60, 0, 12, -20, 0, 0, -4, 0, -30, -12, 0, 0, 6, 0, 0, 10, 10, 0, 0, 0, 0, 0, 0, 10, -6, 0, 0, 4, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 6164566
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 21600, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 21600, 'label': '21600.y.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: 6164577
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 21600, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 10800, 'label': '21600.y.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: 6164588
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 3600, 'counter': 3, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 3600, 'label': '21600.y.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164599
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 4, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 360, 'label': '21600.y.3a1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 6164610
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 5, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 360, 'label': '21600.y.3a2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6164621
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 6, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 360, 'label': '21600.y.3b1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 6164632
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 7, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 360, 'label': '21600.y.3b2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 6164639
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 8, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.b1', 'kernel_order': 180, 'label': '21600.y.3c1', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 2], [1, -2]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 6164640
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 9, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.b1', 'kernel_order': 180, 'label': '21600.y.3c2', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 1], [1, -1]], [[1, 0]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[3, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 6164567
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 10, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 180, 'label': '21600.y.3d1', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 0]], [[1, 1], [1, -1]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 6164568
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 11, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 180, 'label': '21600.y.3d2', 'nt': [12, 76], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 0]], [[1, 2], [1, -2]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 6164569
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 12, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 360, 'label': '21600.y.4a', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6164570
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 13, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 360, 'label': '21600.y.4b', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6164571
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 14, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.b1', 'kernel_order': 180, 'label': '21600.y.4c', 'nt': [10, 11], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6164572
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 15, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 180, 'label': '21600.y.4d', 'nt': [10, 11], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6164573
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 16, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 360, 'label': '21600.y.5a', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164574
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 17, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 360, 'label': '21600.y.5b', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6164575
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 360, 'counter': 18, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.b1', 'kernel_order': 180, 'label': '21600.y.5c', 'nt': [12, 75], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[1, 0]], [[5, 0]], [[-5, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[-5, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164576
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 360, 'counter': 19, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '120.35', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 180, 'label': '21600.y.5d', 'nt': [12, 75], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[-5, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[5, 0]], [[-5, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6164578
    {'center': '360.a1.b1', 'center_index': 360, 'center_order': 60, 'counter': 20, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.b1', 'kernel_order': 60, 'label': '21600.y.6a1', 'nt': [36, 551], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[0, 0]], [[-2, 1], [-2, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164579
    {'center': '360.a1.b1', 'center_index': 360, 'center_order': 60, 'counter': 21, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.b1', 'kernel_order': 60, 'label': '21600.y.6a2', 'nt': [36, 551], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[-2, 2], [-2, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164580
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 60, 'counter': 22, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 60, 'label': '21600.y.6b1', 'nt': [36, 551], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[6, 0]], [[6, 0]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164581
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 60, 'counter': 23, 'cyclotomic_n': 5, 'dim': 6, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 60, 'label': '21600.y.6b2', 'nt': [36, 551], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[6, 0]], [[6, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[-2, 2], [-2, -2]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164582
    {'center': '360.a1.b1', 'center_index': 360, 'center_order': 60, 'counter': 24, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.b1', 'kernel_order': 60, 'label': '21600.y.8a', 'nt': [15, 23], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[8, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164583
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 60, 'counter': 25, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 60, 'label': '21600.y.8b', 'nt': [15, 23], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164584
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 26, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.9a1', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164585
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 27, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.9a2', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164586
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 28, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.9b1', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164587
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 29, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.9b2', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164589
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 30, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.9c1', 'nt': [72, 0], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164590
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 31, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.9c2', 'nt': [72, 0], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164591
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 32, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.9d1', 'nt': [72, 0], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164592
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 33, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.9d2', 'nt': [72, 0], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164593
    {'center': '360.a1.b1', 'center_index': 360, 'center_order': 60, 'counter': 34, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.b1', 'kernel_order': 60, 'label': '21600.y.10a', 'nt': [18, 145], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[2, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-5, 0]], [[-2, 0]], [[10, 0]], [[-5, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164594
    {'center': '360.a1.a1', 'center_index': 360, 'center_order': 60, 'counter': 35, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '360.121', 'image_order': 360, 'indicator': 1, 'kernel': '360.a1.a1', 'kernel_order': 60, 'label': '21600.y.10b', 'nt': [18, 145], 'q_character': None, 'values': [[[10, 0]], [[0, 0]], [[10, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-5, 0]], [[10, 0]], [[-2, 0]], [[1, 0]], [[-5, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164595
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 36, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.12a1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 6164596
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 37, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.12a2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 6164597
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 38, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.12b1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-3, 0]], [[-3, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 6164598
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 39, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.12b2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-3, 0]], [[-3, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 6164600
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 40, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.12c1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[-4, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 6164601
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 41, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.12c2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[-4, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6164602
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 42, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.12d1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-3, 0]], [[-3, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-4, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 6164603
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 43, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.12d2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-3, 0]], [[-3, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-4, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 6164604
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 44, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.15a1', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[-15, 0]], [[-5, 0]], [[3, 0]], [[-3, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[15, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 6164605
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 45, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.15a2', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[-15, 0]], [[-5, 0]], [[3, 0]], [[-3, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[15, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 6164606
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 46, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.15b1', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[-15, 0]], [[3, 0]], [[-5, 0]], [[5, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[15, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 6164607
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 47, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.15b2', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[-15, 0]], [[3, 0]], [[-5, 0]], [[5, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[15, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 6164608
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 48, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.15c1', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-5, 0]], [[3, 0]], [[3, 0]], [[-5, 0]], [[-1, 0]], [[-1, 0]], [[15, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 6164609
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 49, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.15c2', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-5, 0]], [[3, 0]], [[3, 0]], [[-5, 0]], [[-1, 0]], [[-1, 0]], [[15, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 6164611
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 50, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.15d1', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[3, 0]], [[-5, 0]], [[-5, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[15, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 6164612
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 51, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.15d2', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[3, 0]], [[-5, 0]], [[-5, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[15, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 6164613
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 52, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.16a', 'nt': [25, 77], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6164614
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 53, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.16b', 'nt': [50, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6164615
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 54, 'cyclotomic_n': 5, 'dim': 18, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.18a1', 'nt': [180, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-2, 0]], [[2, 0], [-2, 2], [-2, -2]], [[-2, 0]], [[4, 0], [2, 2], [2, -2]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164616
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 55, 'cyclotomic_n': 5, 'dim': 18, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.18a2', 'nt': [180, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-2, 0]], [[4, 0], [2, 2], [2, -2]], [[-2, 0]], [[2, 0], [-2, 2], [-2, -2]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164617
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 56, 'cyclotomic_n': 5, 'dim': 18, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.18b1', 'nt': [180, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[2, 0], [-2, 2], [-2, -2]], [[-2, 0]], [[4, 0], [2, 2], [2, -2]], [[-2, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164618
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 57, 'cyclotomic_n': 5, 'dim': 18, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.18b2', 'nt': [180, 0], 'q_character': None, 'values': [[[18, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[4, 0], [2, 2], [2, -2]], [[-2, 0]], [[2, 0], [-2, 2], [-2, -2]], [[-2, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164619
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 58, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.20a', 'nt': [30, 472], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[5, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[5, 0]], [[-4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6164620
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 59, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.20b', 'nt': [30, 472], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[-4, 0]], [[5, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[5, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164622
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 60, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.20c', 'nt': [60, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[5, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-5, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6164623
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 61, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.20d', 'nt': [60, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[-4, 0]], [[5, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-5, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164624
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 62, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.24a1', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-8, 1], [-8, -1]], [[-8, 2], [-8, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[3, 0]], [[3, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[0, 0]], [[-2, 1], [-2, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164625
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 63, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.24a2', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-8, 2], [-8, -2]], [[-8, 1], [-8, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[3, 0]], [[3, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[-2, 2], [-2, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164626
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 64, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.24b1', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-8, 1], [-8, -1]], [[-8, 2], [-8, -2]], [[-6, 0]], [[-6, 0]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164627
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 65, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.24b2', 'nt': [180, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-8, 2], [-8, -2]], [[-8, 1], [-8, -1]], [[-6, 0]], [[-6, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[-2, 2], [-2, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164628
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 66, 'cyclotomic_n': 1, 'dim': 25, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 6, 'label': '21600.y.25a', 'nt': [36, 4580], 'q_character': None, 'values': [[[25, 0]], [[25, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[25, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164629
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 6, 'counter': 67, 'cyclotomic_n': 1, 'dim': 25, 'faithful': False, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '7200.cz', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 3, 'label': '21600.y.25b', 'nt': [72, 0], 'q_character': None, 'values': [[[25, 0]], [[-25, 0]], [[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[-1, 0]], [[25, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164630
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 68, 'cyclotomic_n': 5, 'dim': 30, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.30a1', 'nt': [216, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[-10, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 1], [-10, -1]], [[-10, 2], [-10, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164631
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 69, 'cyclotomic_n': 5, 'dim': 30, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.30a2', 'nt': [216, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[-10, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-15, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-10, 2], [-10, -2]], [[-10, 1], [-10, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164633
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 70, 'cyclotomic_n': 5, 'dim': 30, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.30b1', 'nt': [216, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[6, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-15, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-10, 1], [-10, -1]], [[-10, 2], [-10, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 1], [5, -1]], [[5, 2], [5, -2]], [[2, 2], [2, -2]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164634
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 71, 'cyclotomic_n': 5, 'dim': 30, 'faithful': True, 'field': [-1, -1, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.30b2', 'nt': [216, 0], 'q_character': None, 'values': [[[30, 0]], [[0, 0]], [[6, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-15, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-10, 2], [-10, -2]], [[-10, 1], [-10, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 2], [5, -2]], [[5, 1], [5, -1]], [[2, 1], [2, -1]], [[0, 0]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164635
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 72, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.32a', 'nt': [75, 0], 'q_character': None, 'values': [[[32, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164636
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 73, 'cyclotomic_n': 1, 'dim': 40, 'faithful': True, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.40a', 'nt': [90, 0], 'q_character': None, 'values': [[[40, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-20, 0]], [[10, 0]], [[-8, 0]], [[4, 0]], [[-5, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164637
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 74, 'cyclotomic_n': 1, 'dim': 40, 'faithful': True, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.40b', 'nt': [90, 0], 'q_character': None, 'values': [[[40, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-20, 0]], [[-8, 0]], [[10, 0]], [[-5, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6164638
    {'center': '21600.a1.a1', 'center_index': 21600, 'center_order': 1, 'counter': 75, 'cyclotomic_n': 1, 'dim': 50, 'faithful': True, 'field': [0, 1], 'group': '21600.y', 'group_counter': 25, 'group_order': 21600, 'image': None, 'image_isoclass': '21600.y', 'image_order': 21600, 'indicator': 1, 'kernel': '21600.a1.a1', 'kernel_order': 1, 'label': '21600.y.50a', 'nt': [108, 0], 'q_character': None, 'values': [[[50, 0]], [[0, 0]], [[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-25, 0]], [[-10, 0]], [[-10, 0]], [[5, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 63947109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 21600, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '21600.y.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': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21600.y', 'subgroup_hash': 6859003311102709662, 'subgroup_order': 21600, 'subgroup_tex': 'S_3\\times A_5^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 10800, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '21600.y.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': False, 'special_labels': ['D', 'S', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10800.u', 'subgroup_hash': 5696638825176348243, 'subgroup_order': 10800, 'subgroup_tex': 'A_5\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3600, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7200.cz', 'subgroup_hash': 1011210826241093481, 'subgroup_order': 7200, 'subgroup_tex': 'C_2\\times A_5^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 360, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.ct', 'subgroup_hash': 1199672556059335690, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times A_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 360, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4320.ct', 'subgroup_hash': 1199672556059335690, 'subgroup_order': 4320, 'subgroup_tex': 'S_3\\times A_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 3600, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '21600.y.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': False, 'special_labels': ['PC', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3600.a', 'subgroup_hash': 8673234499945238871, 'subgroup_order': 3600, 'subgroup_tex': 'A_5^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 360, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.6.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3600.de', 'subgroup_hash': 4043447238585440586, 'subgroup_order': 3600, 'subgroup_tex': '\\GL(2,4):D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 63947869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 360, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.6.b1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3600.de', 'subgroup_hash': 4043447238585440586, 'subgroup_order': 3600, 'subgroup_tex': '\\GL(2,4):D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 63947880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 360, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.10.a1.a1', 'maximal': True, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cm', 'subgroup_hash': 6018971842015229741, 'subgroup_order': 2160, 'subgroup_tex': 'S_3^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 360, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.10.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.cm', 'subgroup_hash': 6018971842015229741, 'subgroup_order': 2160, 'subgroup_tex': 'S_3^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 180, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.dj', 'subgroup_hash': 6379761567884029730, 'subgroup_order': 2160, 'subgroup_tex': 'A_4\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 180, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2160.dj', 'subgroup_hash': 6379761567884029730, 'subgroup_order': 2160, 'subgroup_tex': 'A_4\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 360, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.560', 'subgroup_hash': 560, 'subgroup_order': 1800, 'subgroup_tex': '\\GL(2,4):C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 63947154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 360, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.560', 'subgroup_hash': 560, 'subgroup_order': 1800, 'subgroup_tex': '\\GL(2,4):C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 63947165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 180, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.562', 'subgroup_hash': 562, 'subgroup_order': 1800, 'subgroup_tex': 'D_{15}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 180, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.562', 'subgroup_hash': 562, 'subgroup_order': 1800, 'subgroup_tex': 'D_{15}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 180, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.561', 'subgroup_hash': 561, 'subgroup_order': 1800, 'subgroup_tex': 'D_5\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 180, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.561', 'subgroup_hash': 561, 'subgroup_order': 1800, 'subgroup_tex': 'D_5\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5850', 'subgroup_hash': 5850, 'subgroup_order': 1440, 'subgroup_tex': 'C_2^3:\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.15.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5850', 'subgroup_hash': 5850, 'subgroup_order': 1440, 'subgroup_tex': 'C_2^3:\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 360, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.15.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5853', 'subgroup_hash': 5853, 'subgroup_order': 1440, 'subgroup_tex': '\\GL(2,4):C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 63947243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 360, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.15.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5853', 'subgroup_hash': 5853, 'subgroup_order': 1440, 'subgroup_tex': '\\GL(2,4):C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 63947254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1200.944', 'subgroup_hash': 944, 'subgroup_order': 1200, 'subgroup_tex': 'D_{10}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1200.944', 'subgroup_hash': 944, 'subgroup_order': 1200, 'subgroup_tex': 'D_{10}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 360, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.492', 'subgroup_hash': 492, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 360, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.20.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.492', 'subgroup_hash': 492, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 180, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.491', 'subgroup_hash': 491, 'subgroup_order': 1080, 'subgroup_tex': '\\GL(2,4):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63947309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 180, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.491', 'subgroup_hash': 491, 'subgroup_order': 1080, 'subgroup_tex': '\\GL(2,4):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 63947320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 180, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.492', 'subgroup_hash': 492, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 180, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.20.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1080.492', 'subgroup_hash': 492, 'subgroup_order': 1080, 'subgroup_tex': 'S_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 180, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.88', 'subgroup_hash': 88, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 180, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.88', 'subgroup_hash': 88, 'subgroup_order': 900, 'subgroup_tex': 'C_{15}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '21600.y.25.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '25.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': 25, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4680', 'subgroup_hash': 4680, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '720.797', 'subgroup_hash': 797, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '720.797', 'subgroup_hash': 797, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 360, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 360, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 180, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947454
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 180, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.771', 'subgroup_hash': 771, 'subgroup_order': 720, 'subgroup_tex': 'D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947465
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 180, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.772', 'subgroup_hash': 772, 'subgroup_order': 720, 'subgroup_tex': 'C_2^2\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 180, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.772', 'subgroup_hash': 772, 'subgroup_order': 720, 'subgroup_tex': 'C_2^2\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 60, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.768', 'subgroup_hash': 768, 'subgroup_order': 720, 'subgroup_tex': 'A_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 60, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.768', 'subgroup_hash': 768, 'subgroup_order': 720, 'subgroup_tex': 'A_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.768', 'subgroup_hash': 768, 'subgroup_order': 720, 'subgroup_tex': 'A_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.30.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.768', 'subgroup_hash': 768, 'subgroup_order': 720, 'subgroup_tex': 'A_4\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 60, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.147', 'subgroup_hash': 147, 'subgroup_order': 600, 'subgroup_tex': 'C_{10}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 60, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.36.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.147', 'subgroup_hash': 147, 'subgroup_order': 600, 'subgroup_tex': 'C_{10}\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '600.174', 'subgroup_hash': 174, 'subgroup_order': 600, 'subgroup_tex': 'S_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.146', 'subgroup_hash': 146, 'subgroup_order': 600, 'subgroup_tex': 'D_5\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.146', 'subgroup_hash': 146, 'subgroup_order': 600, 'subgroup_tex': 'D_5\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.146', 'subgroup_hash': 146, 'subgroup_order': 600, 'subgroup_tex': 'D_5\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.146', 'subgroup_hash': 146, 'subgroup_order': 600, 'subgroup_tex': 'D_5\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 180, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.88', 'subgroup_hash': 88, 'subgroup_order': 540, 'subgroup_tex': 'C_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 180, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '540.88', 'subgroup_hash': 88, 'subgroup_order': 540, 'subgroup_tex': 'C_3\\times \\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1187', 'subgroup_hash': 1187, 'subgroup_order': 480, 'subgroup_tex': 'C_2^3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.45.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1187', 'subgroup_hash': 1187, 'subgroup_order': 480, 'subgroup_tex': 'C_2^3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.50.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.50.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.750', 'subgroup_hash': 750, 'subgroup_order': 432, 'subgroup_tex': 'C_3\\times A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 60, 'characteristic': False, 'core_order': 360, 'counter': 62, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '21600.y.60.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'A_5', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 60, 'characteristic': False, 'core_order': 360, 'counter': 63, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '21600.y.60.a1.b1', 'maximal': False, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'A_5', 'simple': False, 'solvable': False, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.122', 'subgroup_hash': 122, 'subgroup_order': 360, 'subgroup_tex': 'C_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.122', 'subgroup_hash': 122, 'subgroup_order': 360, 'subgroup_tex': 'C_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947731
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '360.143', 'subgroup_hash': 143, 'subgroup_order': 360, 'subgroup_tex': 'C_5\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '360.143', 'subgroup_hash': 143, 'subgroup_order': 360, 'subgroup_tex': 'C_5\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '360.137', 'subgroup_hash': 137, 'subgroup_order': 360, 'subgroup_tex': 'D_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '360.137', 'subgroup_hash': 137, 'subgroup_order': 360, 'subgroup_tex': 'D_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.e1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.e1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '360.144', 'subgroup_hash': 144, 'subgroup_order': 360, 'subgroup_tex': 'A_4\\times D_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 63947809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '360.144', 'subgroup_hash': 144, 'subgroup_order': 360, 'subgroup_tex': 'A_4\\times D_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 63947820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '360.142', 'subgroup_hash': 142, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '360.142', 'subgroup_hash': 142, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 180, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 180, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 60, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947871
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 60, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 180, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.122', 'subgroup_hash': 122, 'subgroup_order': 360, 'subgroup_tex': 'C_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 180, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.122', 'subgroup_hash': 122, 'subgroup_order': 360, 'subgroup_tex': 'C_6\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 60, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.60.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.37', 'subgroup_hash': 37, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.37', 'subgroup_hash': 37, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '300.38', 'subgroup_hash': 38, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '300.39', 'subgroup_hash': 39, 'subgroup_order': 300, 'subgroup_tex': 'D_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.39', 'subgroup_hash': 39, 'subgroup_order': 300, 'subgroup_tex': 'D_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947882
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 60, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.22', 'subgroup_hash': 22, 'subgroup_order': 300, 'subgroup_tex': 'C_5\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 60, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.22', 'subgroup_hash': 22, 'subgroup_order': 300, 'subgroup_tex': 'C_5\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.40', 'subgroup_hash': 40, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.75.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.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': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1029', 'subgroup_hash': 1029, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.75.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.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': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.75.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.75.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.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': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.75.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '240.198', 'subgroup_hash': 198, 'subgroup_order': 240, 'subgroup_tex': 'A_4\\times D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 63947112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '240.198', 'subgroup_hash': 198, 'subgroup_order': 240, 'subgroup_tex': 'A_4\\times D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 63947113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '240.202', 'subgroup_hash': 202, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '240.202', 'subgroup_hash': 202, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 60, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 60, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.90.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.100.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.100.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 63947125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.100.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.100.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.100.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.100.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63947129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.49', 'subgroup_hash': 49, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 180, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '21600.y.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_5', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 180, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '21600.y.120.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_5', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 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': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.28', 'subgroup_hash': 28, 'subgroup_order': 180, 'subgroup_tex': 'C_5\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.29', 'subgroup_hash': 29, 'subgroup_order': 180, 'subgroup_tex': 'S_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '180.31', 'subgroup_hash': 31, 'subgroup_order': 180, 'subgroup_tex': 'A_4\\times C_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 63947142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.31', 'subgroup_hash': 31, 'subgroup_order': 180, 'subgroup_tex': 'A_4\\times C_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 63947144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.27', 'subgroup_hash': 27, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 60, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 60, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 60, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 60, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '180.30', 'subgroup_hash': 30, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '180.30', 'subgroup_hash': 30, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.120.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 63947157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': False, 'core_order': 6, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.10', 'subgroup_hash': 10, 'subgroup_order': 150, 'subgroup_tex': 'S_3\\times C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947159
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.144.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947160
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.144.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '150.11', 'subgroup_hash': 11, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '150.12', 'subgroup_hash': 12, 'subgroup_order': 150, 'subgroup_tex': 'C_5:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': 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: 63947166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': 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: 63947167
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': 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: 63947168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': 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: 63947169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': 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: 63947172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': 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: 63947173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.f1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.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': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.150.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 63947183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.43', 'subgroup_hash': 43, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.43', 'subgroup_hash': 43, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 60, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 60, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947195
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.46', 'subgroup_hash': 46, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.46', 'subgroup_hash': 46, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947206
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.42', 'subgroup_hash': 42, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.44', 'subgroup_hash': 44, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.44', 'subgroup_hash': 44, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 60, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947216
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 60, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947217
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 60, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.180.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947228
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.200.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.14', 'subgroup_hash': 14, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.216.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.14', 'subgroup_hash': 14, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.216.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.225.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.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': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.225.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.225.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.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': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.225.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.225.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.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': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 6, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 6, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 3, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '90.8', 'subgroup_hash': 8, 'subgroup_order': 90, 'subgroup_tex': 'C_{15}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.240.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '90.9', 'subgroup_hash': 9, 'subgroup_order': 90, 'subgroup_tex': 'C_3:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.270.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': 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: 63947259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.270.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '270.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 270, 'quotient_simple': 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: 63947260
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 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': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947261
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947262
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947263
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947264
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947269
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.h1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': 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: 63947299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.300.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': 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: 63947300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 360, 'characteristic': False, 'core_order': 60, 'counter': 271, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '21600.y.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '360.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '360.121', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 121, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 360, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times A_5', 'simple': True, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 360, 'characteristic': False, 'core_order': 60, 'counter': 272, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '21600.y.360.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '360.a1.b1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '360.121', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 121, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 360, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times A_5', 'simple': True, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 6, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947328
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.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': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947329
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.9', 'subgroup_hash': 9, 'subgroup_order': 60, 'subgroup_tex': 'C_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.9', 'subgroup_hash': 9, 'subgroup_order': 60, 'subgroup_tex': 'C_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.9', 'subgroup_hash': 9, 'subgroup_order': 60, 'subgroup_tex': 'C_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.9', 'subgroup_hash': 9, 'subgroup_order': 60, 'subgroup_tex': 'C_5\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.v1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.v1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.v1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.v1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.y1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.360.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.y1.b1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63947358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.400.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.400.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.400.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.400.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.400.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947366
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63947367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.432.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.432.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.432.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': 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: 63947375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': 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: 63947378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': 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: 63947381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': 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: 63947384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': 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: 63947386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63947388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': 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: 63947390
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': 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: 63947391
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': 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: 63947392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.k1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.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': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.450.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 3, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 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': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947397
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 3, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.480.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 63947400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': 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: 63947401
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 63947402
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '540.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': 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: 63947403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 63947404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': 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: 63947405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 63947406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': 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: 63947407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 63947408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': 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: 63947410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 63947411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': 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: 63947412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.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': 540, 'quotient_simple': 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: 63947413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.540.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '540.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 540, 'quotient_simple': 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: 63947414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947433
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947434
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947446
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947457
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947459
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947460
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947461
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.w1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.w1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947463
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.w1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.w1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947464
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': 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: 63947467
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': 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: 63947468
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.600.z1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.z1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63947470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '21600.y.675.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '675.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': 675, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 2}
  • id: 63947471
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.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': 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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947472
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.720.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947473
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 6, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947474
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 300, 'characteristic': False, 'core_order': 6, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947475
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': False, 'core_order': 6, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947477
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 25, 'characteristic': False, 'core_order': 6, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947478
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 431, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947479
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 432, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.720.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 63947480
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947481
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947482
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947483
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947484
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947485
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947486
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947488
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947489
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947490
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 3, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947491
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947492
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947493
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947494
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 63947495
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947496
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947497
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947499
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947500
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947501
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947502
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947503
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947504
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947505
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947506
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947507
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947508
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947510
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947511
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947512
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947513
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947514
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.720.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 63947515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '21600.y.800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '800.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': 800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 63947516
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 5, 'label': '21600.y.864.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
  • id: 63947517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947519
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947527
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947529
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.f1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.f1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947530
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.k1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.k1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.k1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947564
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.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': 900, 'quotient_simple': None, '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: 63947573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.900.z1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.z1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, '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: 63947574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947575
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947592
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947593
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1080.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947595
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.l1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.l1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': 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: 63947604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1080.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1080, 'quotient_simple': 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: 63947605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 6, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 6, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947610
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947611
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947622
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947624
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1200, 'quotient_simple': 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: 63947637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947638
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1200.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 1200, 'quotient_simple': 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: 63947639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1350.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1350.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': 1350, 'quotient_simple': 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: 63947640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1350.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1350.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': 1350, 'quotient_simple': 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: 63947641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1350.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1350.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': 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: 63947643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1350.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1350.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': 1350, 'quotient_simple': 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: 63947644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1350.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1350.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': 1350, 'quotient_simple': 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: 63947645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1350.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1350.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1350, 'quotient_simple': 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: 63947646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1350.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1350.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': 1350, 'quotient_simple': 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: 63947647
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 900, 'characteristic': False, 'core_order': 3, 'counter': 584, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63947648
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 900, 'characteristic': False, 'core_order': 3, 'counter': 585, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': 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: 63947649
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 586, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63947650
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 587, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': 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: 63947651
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63947652
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': 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: 63947654
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63947655
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.1440.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': 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: 63947656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947678
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 3, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 3, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947702
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947703
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947707
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947711
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947712
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.ba1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ba1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947714
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.ba1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.ba1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bb1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bb1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947718
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bb1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bb1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.be1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.be1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bf1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.bf1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947728
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bg1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947729
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.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': 1800, 'quotient_simple': None, '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: 63947730
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.1800.bh1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1800.bh1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, '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: 63947732
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 1, 'counter': 660, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947733
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 1, 'counter': 661, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947734
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 662, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947735
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 663, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947736
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947737
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947738
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947739
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947740
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 668, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947741
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.2160.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947743
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947744
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947745
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947746
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947747
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947748
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947749
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947750
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947751
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 63947752
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2160.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 63947754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 3, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2400.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': 2400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 3, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2400.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2400.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2400.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': 2400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2400.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2400.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': 2400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2400.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2400.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2400.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2400.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': 2400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2400.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2400.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': 2400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 63947761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947762
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947763
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947766
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.d1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947769
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947770
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.e1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.e1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947777
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947782
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947785
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.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': 2700, 'quotient_simple': 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: 63947786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.2700.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2700.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2700, 'quotient_simple': 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: 63947788
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': True, 'centralizer_order': 3600, 'characteristic': True, 'core_order': 6, 'counter': 710, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '21600.y.3600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3600.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3600.a', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8673234499945238871, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3600, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'A_5^2', 'simple': False, 'solvable': True, 'special_labels': ['R', 'C2'], '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: 63947789
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947790
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947791
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947792
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 3, 'counter': 714, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947793
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 720, 'characteristic': False, 'core_order': 3, 'counter': 715, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947794
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947795
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947796
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947797
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947799
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947800
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947801
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947802
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947803
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947804
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947805
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947806
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947807
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947808
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947810
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 730, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.3600.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947811
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947812
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947813
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947814
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947815
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947816
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947817
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947818
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3600, 'quotient_simple': 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: 63947819
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947821
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.3600.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3600.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': 3600, 'quotient_simple': 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: 63947822
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1800, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.4320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.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': 4320, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1800, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.4320.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947824
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.4320.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.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': 4320, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947825
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 744, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.4320.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 63947826
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947827
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947828
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947832
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947833
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947835
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947839
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 1, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 1, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.i1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.i1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.k1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947849
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.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': 5400, 'quotient_simple': 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: 63947850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21600.y.5400.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5400.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5400, 'quotient_simple': 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: 63947851
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 10800, 'characteristic': True, 'core_order': 3, 'counter': 768, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '21600.y.7200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '7200.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '7200.cz', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1011210826241093481, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 7200, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_5^2', 'simple': True, 'solvable': True, 'special_labels': ['F', 'C3'], '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: 63947852
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1080, 'characteristic': False, 'core_order': 1, 'counter': 769, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.7200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7200.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': 7200, '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: 63947854
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1080, 'characteristic': False, 'core_order': 1, 'counter': 770, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.7200.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7200.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7200, '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: 63947855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 1, 'counter': 771, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.7200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7200.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': 7200, '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: 63947856
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 540, 'characteristic': False, 'core_order': 1, 'counter': 772, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.7200.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7200.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7200, '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: 63947857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.7200.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7200.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': 7200, '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: 63947858
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 774, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.7200.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7200.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': 7200, '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: 63947859
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 7200, 'characteristic': False, 'core_order': 1, 'counter': 775, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.10800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.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': 10800, '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: 63947860
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 1, 'counter': 776, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.10800.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.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': 10800, '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: 63947861
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 1, 'counter': 777, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.10800.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, '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: 63947862
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 778, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.10800.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.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': 10800, '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: 63947863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 779, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.10800.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10800, '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: 63947865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 780, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.10800.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.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': 10800, '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: 63947866
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 781, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '21600.y.10800.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10800.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': 10800, '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: 63947867
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '21600.y', 'ambient_counter': 25, 'ambient_order': 21600, 'ambient_tex': 'S_3\\times A_5^2', 'central': True, 'central_factor': False, 'centralizer_order': 21600, 'characteristic': True, 'core_order': 1, 'counter': 782, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '21600.y.21600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '21600.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '21600.y', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6859003311102709662, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 21600, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times A_5^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'C4'], '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: 63947109
    {'ambient': '21600.y', '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': '21600.a1.a1', 'complements': ['21600.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '5.a1.a1', '5.a1.b1', '6.b1.a1', '6.b1.b1', '10.a1.a1', '10.a1.b1', '60.e1.a1', '60.e1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5445, 7204, 6056, 5944, 5472, 5127, 2759, 5601], 'generators': [39916800, 1963808793, 43545600, 40222474], 'label': '21600.y.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '60.a1.a1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '21600.y', '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': '21600.y'}
  • id: 63947110
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.b1', '30.a1.b1', '30.c1.b1', '50.a1.b1', '60.d1.b1', '100.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5394, -1, 5514, -1, 5095, -1, 4090, -1], 'generators': [39916800, 43545600, 83484144, 1584, 80081432, 5792221743], 'label': '21600.y.10.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '10.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2160.cm'}
  • id: 63947111
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '18.a1.b1', '30.b1.a1'], 'contains': ['180.a1.a1', '180.i1.a1', '180.m1.a1', '270.a1.a1', '360.c1.b1', '450.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5014, -1, 3984, -1, 4084, -1, 2452, -1], 'generators': [4834258861, 2424, 1680, 5875684380, 83463240, 83462400], 'label': '21600.y.90.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '21600.y', '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': '120.39'}
  • id: 63947112
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '18.a1.a1', '30.b1.b1'], 'contains': ['180.a1.b1', '180.i1.b1', '180.m1.b1', '270.a1.b1', '360.c1.a1', '450.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5014, -1, 6382, -1, 4084, -1, 4261, -1], 'generators': [4834218540, 2043625110, 2043383282, 1959914882, 5396700062, 83462400], 'label': '21600.y.90.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.b1', 'old_label': '90.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.b1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 63947113
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.a1.a1', '30.c1.a1', '45.a1.a1'], 'contains': ['180.c1.b1', '180.o1.b1', '180.p1.a1', '450.a1.a1', '540.c1.a1', '900.e1.a1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 45, 'diagramx': [5880, -1, 4342, -1, 4709, -1, 2650, -1], 'generators': [5791975591, 5396684222, 1680, 83462400], 'label': '21600.y.90.b1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.b1.a1', 'projective_image': '21600.y', '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': '60.5'}
  • id: 63947114
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '30.a1.b1', '30.c1.b1', '45.a1.b1'], 'contains': ['180.c1.a1', '180.o1.a1', '180.p1.b1', '450.a1.b1', '540.c1.b1', '900.e1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5880, -1, 4404, -1, 4709, -1, 4417, -1], 'generators': [3628800, 4834218540, 4834225140, 4837858164], 'label': '21600.y.90.b1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.b1', 'old_label': '90.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947115
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.a1', '30.b1.a1'], 'contains': ['180.e1.a1', '180.f1.a1', '180.g1.a1', '180.h1.a1', '180.j1.a1', '180.k1.a1', '180.l1.a1', '270.a1.a1', '450.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4699, -1, 2631, -1, 3511, -1, 2224, -1], 'generators': [39916800, 43545600, 4914092461, 2424, 1680, 5792223420], 'label': '21600.y.90.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '90.c1.a1', 'projective_image': '21600.y', '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': '180.26'}
  • id: 63947116
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.b1', '30.b1.b1'], 'contains': ['180.e1.b1', '180.f1.b1', '180.g1.b1', '180.h1.b1', '180.j1.b1', '180.k1.b1', '180.l1.b1', '270.a1.b1', '450.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [4699, -1, 6256, -1, 3511, -1, 3949, -1], 'generators': [4877764140, 39916800, 43545600, 2043383282, 1959914882, 5396700062], 'label': '21600.y.90.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '90.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.b1', 'subgroup_fusion': None, 'weyl_group': '180.26'}
  • id: 63947117
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '45.a1.a1'], 'contains': ['180.o1.b1', '180.p1.a1', '450.f1.a1', '540.f1.a1', '900.u1.a1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 45, 'diagramx': [3268, -1, 4730, -1, 5236, -1, 2699, -1], 'generators': [5875437991, 5396684222, 83464080, 2424], 'label': '21600.y.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': '21600.y', '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': '60.5'}
  • id: 63947118
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.b1', '45.a1.b1'], 'contains': ['180.o1.a1', '180.p1.b1', '450.f1.b1', '540.f1.b1', '900.u1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [3268, -1, 7433, -1, 5236, -1, 4466, -1], 'generators': [5396689142, 4834218540, 2043377282, 5396693366], 'label': '21600.y.90.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.b1', 'old_label': '90.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947119
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '30.f1.a1', '30.g1.a1', '45.a1.a1'], 'contains': ['180.p1.a1', '450.i1.b1', '540.g1.a1', '900.y1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1170, -1, 5505, -1, 6189, -1, 2748, -1], 'generators': [5791975591, 2424, 5313221822, 1680], 'label': '21600.y.90.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '90.e1.a1', 'projective_image': '21600.y', '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': '180.19'}
  • id: 63947120
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.b1', '30.f1.b1', '30.g1.b1', '45.a1.b1'], 'contains': ['180.p1.b1', '450.i1.a1', '540.g1.b1', '900.y1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1170, -1, 8655, -1, 6189, -1, 4515, -1], 'generators': [4834218540, 5313226742, 1959914882, 5313230966], 'label': '21600.y.90.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '90.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.e1.b1', 'subgroup_fusion': None, 'weyl_group': '180.19'}
  • id: 63947121
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['30.e1.a1', '30.f1.a1', '30.g1.a1', '40.a1.b1', '50.b1.a1', '60.g1.a1', '100.d1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1627, -1, 7774, -1, 5728, -1, 2606, -1], 'generators': [5313220382, 43545600, 5835519751, 2424, 79834440, 1680], 'label': '21600.y.10.b1.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.b1.a1', 'projective_image': '21600.y', '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': '1440.5850'}
  • id: 63947122
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '25.a1.a1', '50.a1.b1'], 'contains': ['200.d1.a1', '300.a1.a1', '300.d1.a1', '300.e1.a1', '300.f1.a1', '400.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3014, -1, 6134, -1, 6956, -1, 5730, -1], 'generators': [39916800, 43545600, 5875396137, 2424, 1680, 83463240], 'label': '21600.y.100.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '100.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.190'}
  • id: 63947123
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '25.a1.a1', '50.a1.a1'], 'contains': ['200.d1.b1', '300.a1.b1', '300.d1.b1', '300.e1.b1', '300.f1.b1', '400.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3014, -1, 8033, -1, 6956, -1, 4776, -1], 'generators': [39916800, 5356806064, 83462640, 43545600, 5875396137, 5832179105], 'label': '21600.y.100.a1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1.b1', 'subgroup_fusion': None, 'weyl_group': '144.190'}
  • id: 63947124
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '10.a1.b1'], 'contains': ['200.a1.a1', '200.a1.b1', '200.b1.a1', '200.c1.a1', '200.c1.b1', '200.e1.a1', '200.f1.a1', '300.b1.a1', '300.g1.a1', '300.g1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6194, -1, 6516, -1, 5528, -1, 4960, -1], 'generators': [83479080, 39916800, 43545600, 15988, 2043377281, 83478384], 'label': '21600.y.100.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '100.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 63947125
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '100.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '50.a1.b1'], 'contains': ['200.d1.a1', '300.j1.a1', '300.k1.a1', '300.l1.a1', '300.m1.a1', '400.c1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3861, -1, 6755, -1, 5745, -1, 5671, -1], 'generators': [43545600, 5832138543, 2424, 79834440, 1680, 5392806153], 'label': '21600.y.100.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '100.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.749'}
  • id: 63947126
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '100.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.b1', '50.a1.a1'], 'contains': ['200.d1.b1', '300.j1.b1', '300.k1.b1', '300.l1.b1', '300.m1.b1', '400.c1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3861, -1, 8359, -1, 5745, -1, 4717, -1], 'generators': [4877764140, 298230, 43545600, 2003708310, 1959914882, 4837852404], 'label': '21600.y.100.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.c1.b1', 'subgroup_fusion': None, 'weyl_group': '432.749'}
  • id: 63947127
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '100.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '20.c1.a1', '50.a1.a1'], 'contains': ['200.d1.b1', '300.o1.a1', '300.p1.a1', '300.q1.a1', '300.r1.a1', '400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1283, -1, 8638, -1, 6687, -1, 4657, -1], 'generators': [4877764140, 4877769204, 298230, 43545600, 2003708310, 1959914882], 'label': '21600.y.100.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '100.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.190'}
  • id: 63947128
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '100.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '20.c1.b1', '50.a1.b1'], 'contains': ['200.d1.a1', '300.o1.b1', '300.p1.b1', '300.q1.b1', '300.r1.b1', '400.b1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1283, -1, 8555, -1, 6687, -1, 5545, -1], 'generators': [43545600, 2424, 79834440, 1680, 5792221743, 5392806153], 'label': '21600.y.100.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '100.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.d1.b1', 'subgroup_fusion': None, 'weyl_group': '144.190'}
  • id: 63947129
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.a1.b1', '36.b1.a1'], 'contains': ['216.a1.a1', '216.a1.b1', '216.b1.a1', '216.c1.a1', '216.c1.b1', '216.d1.a1', '216.e1.a1', '540.c1.a1', '540.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8677, -1, 2104, -1, 361, -1, 559, -1], 'generators': [3628800, 1963543685, 5795890862, 4837869084, 12360], 'label': '21600.y.108.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947130
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.b1', 'complements': ['180.d1.b1', '180.d1.a1', '180.o1.b1', '180.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.h1.a1', '60.k1.b1'], 'contains': ['360.a1.a1', '600.o1.a1', '720.f1.a1', '1200.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5373, 4796, 8186, 6213, 4166, 5236, 3493, 6289], 'generators': [43545600, 79844424, 6600], 'label': '21600.y.120.a1.a1', 'mobius_quo': 1, 'mobius_sub': 60, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['2.a1.a1', '60.a1.a1'], 'normal_contains': ['360.a1.a1', '7200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': '120.35', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947131
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.a1', 'complements': ['180.d1.a1', '180.d1.b1', '180.c1.a1', '180.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '40.a1.b1', '60.a1.b1', '60.h1.b1', '60.k1.a1'], 'contains': ['360.a1.b1', '600.o1.b1', '720.f1.b1', '1200.e1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5373, 4796, 6164, 2904, 4166, 5236, 1461, 3196], 'generators': [5393053742, 43545600, 5835519511], 'label': '21600.y.120.a1.b1', 'mobius_quo': 1, 'mobius_sub': 60, 'normal_closure': '120.a1.b1', 'normal_contained_in': ['2.a1.a1', '60.a1.b1'], 'normal_contains': ['360.a1.b1', '7200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': '120.35', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '120.a1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947132
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.b1'], 'contains': ['30.e1.b1', '30.f1.b1', '30.g1.b1', '40.a1.a1', '50.b1.a1', '60.g1.b1', '100.d1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1627, -1, 8384, -1, 5728, -1, 4271, -1], 'generators': [5393064566, 4877764140, 43545600, 2003708310, 5392772192, 1959914882], 'label': '21600.y.10.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1440.5850'}
  • id: 63947133
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.d1.b1', '360.b1.a1', '360.e1.a1', '600.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8075, -1, 3745, -1, 1701, -1, 1182, -1], 'generators': [39916800, 43545600, 5832191126, 5872097246, 5832178862], 'label': '21600.y.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947134
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '60.d1.b1'], 'contains': ['240.a1.b1', '240.b1.b1', '240.d1.a1', '360.b1.b1', '360.e1.b1', '600.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8075, -1, 1081, -1, 1701, -1, 3005, -1], 'generators': [1959936721, 39916800, 43545600, 1963813350, 83472720], 'label': '21600.y.120.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947135
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '30.b1.b1', '60.d1.b1'], 'contains': ['240.a1.b1', '240.c1.a1', '240.e1.b1', '360.c1.a1', '360.f1.a1', '600.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5103, -1, 740, -1, 1347, -1, 3139, -1], 'generators': [39916800, 43545600, 1963791510, 17520, 83468400], 'label': '21600.y.120.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.c1.a1', 'projective_image': '21600.y', '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': '120.42'}
  • id: 63947136
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '30.b1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.c1.b1', '240.e1.a1', '360.c1.b1', '360.f1.b1', '600.c1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5103, -1, 4108, -1, 1347, -1, 1305, -1], 'generators': [39916800, 83462640, 43545600, 4914092461, 5875684380], 'label': '21600.y.120.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 63947137
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.a1'], 'contains': ['240.a1.a1', '240.f1.a1', '240.g1.a1', '360.d1.a1', '360.g1.a1', '600.e1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7746, -1, 4060, -1, 2516, -1, 1401, -1], 'generators': [39916800, 43545600, 5872097246, 5832178862, 4877776404], 'label': '21600.y.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.d1.a1', 'projective_image': '21600.y', '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': '360.137'}
  • id: 63947138
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.b1'], 'contains': ['240.a1.b1', '240.f1.b1', '240.g1.b1', '360.d1.b1', '360.g1.b1', '600.e1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7746, -1, 3307, -1, 2516, -1, 3300, -1], 'generators': [39916800, 43545600, 1963813350, 1959937465, 83472720], 'label': '21600.y.120.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.b1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
  • id: 63947139
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '60.d1.a1'], 'contains': ['240.b1.a1', '240.e1.a1', '240.g1.a1', '360.j1.a1', '360.m1.a1', '600.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7851, -1, 3965, -1, 2417, -1, 1056, -1], 'generators': [2043377285, 43545600, 4837859604, 4837848924, 5792262062], 'label': '21600.y.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.e1.a1', 'projective_image': '21600.y', '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': '360.137'}
  • id: 63947140
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '60.d1.b1'], 'contains': ['240.b1.b1', '240.e1.b1', '240.g1.b1', '360.j1.b1', '360.m1.b1', '600.k1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7851, -1, 2231, -1, 2417, -1, 2955, -1], 'generators': [43545600, 1963814094, 79843920, 1999854265, 39921960], 'label': '21600.y.120.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.b1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
  • id: 63947141
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.c1.a1', '60.f1.a1', '60.g1.a1'], 'contains': ['360.n1.a1', '360.o1.a1', '360.p1.a1', '480.a1.a1', '600.o1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6404, -1, 5497, -1, 3715, -1, 1107, -1], 'generators': [5872055580, 43545600, 2424, 79834440, 1680], 'label': '21600.y.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.f1.a1', 'projective_image': '21600.y', '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': '48.49'}
  • id: 63947142
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '60.c1.b1', '60.f1.b1', '60.g1.b1'], 'contains': ['360.n1.b1', '360.o1.b1', '360.p1.b1', '480.a1.b1', '600.o1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6404, -1, 7497, -1, 3715, -1, 3055, -1], 'generators': [4877764140, 43545600, 2039754482, 2003708310, 1959914882], 'label': '21600.y.120.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '120.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.b1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63947143
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1'], 'contains': ['24.a1.a1', '36.a1.a1', '60.a1.a1', '60.c1.a1', '72.a1.a1', '120.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6222, -1, 2386, -1, 2833, -1, 1871, -1], 'generators': [5872107182, 39916800, 5872097846, 43545600, 5832178862], 'label': '21600.y.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.a1.a1', 'projective_image': '21600.y', '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': '720.771'}
  • id: 63947144
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '60.d1.b1'], 'contains': ['240.c1.a1', '240.d1.a1', '240.g1.b1', '360.q1.a1', '360.r1.a1', '360.s1.a1', '600.h1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6160, -1, 2140, -1, 2271, -1, 3248, -1], 'generators': [5160, 43545600, 79843920, 1999854265, 2003730894], 'label': '21600.y.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.g1.a1', 'projective_image': '21600.y', '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': '360.137'}
  • id: 63947145
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.b1', '60.d1.a1'], 'contains': ['240.c1.b1', '240.d1.b1', '240.g1.a1', '360.q1.b1', '360.r1.b1', '360.s1.b1', '600.h1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6160, -1, 4345, -1, 2271, -1, 1233, -1], 'generators': [43545600, 4837859604, 2039748485, 5792262062, 4877765724], 'label': '21600.y.120.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.b1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
  • id: 63947146
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '20.c1.a1', '60.d1.a1'], 'contains': ['240.b1.a1', '240.c1.b1', '240.f1.a1', '360.t1.a1', '360.u1.a1', '600.u1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2446, -1, 5197, -1, 2805, -1, 984, -1], 'generators': [43545600, 4877776404, 2039748485, 5792262062, 4877765724], 'label': '21600.y.120.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.h1.a1', 'projective_image': '21600.y', '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': '120.42'}
  • id: 63947147
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.c1.b1', '60.d1.b1'], 'contains': ['240.b1.b1', '240.c1.a1', '240.f1.b1', '360.t1.b1', '360.u1.b1', '600.u1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2446, -1, 4758, -1, 2805, -1, 2883, -1], 'generators': [5160, 43545600, 1959937465, 79843920, 2003730894], 'label': '21600.y.120.h1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 63947148
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.b1', '40.a1.a1', '60.i1.a1'], 'contains': ['360.a1.a1', '600.r1.a1', '720.h1.a1', '1200.f1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2536, -1, 8240, -1, 4709, -1, 3937, -1], 'generators': [10824, 5356484192, 5356477592], 'label': '21600.y.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '120.i1.a1', 'projective_image': '21600.y', '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': '120.35'}
  • id: 63947149
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '40.a1.b1', '60.i1.b1'], 'contains': ['360.a1.b1', '600.r1.b1', '720.h1.b1', '1200.f1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 20, 'diagramx': [2536, -1, 8752, -1, 4709, -1, 2039, -1], 'generators': [79833840, 5871807751, 5393053982], 'label': '21600.y.120.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.b1', 'old_label': '120.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947150
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.b1', '40.a1.a1', '60.b1.a1', '60.j1.a1', '60.l1.b1'], 'contains': ['360.a1.a1', '600.s1.a1', '720.g1.a1', '1200.g1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2297, -1, 8315, -1, 4966, -1, 4257, -1], 'generators': [10824, 5312938592, 5312931992], 'label': '21600.y.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '120.j1.a1', 'projective_image': '21600.y', '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': '120.35'}
  • id: 63947151
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '40.a1.b1', '60.b1.b1', '60.j1.b1', '60.l1.a1'], 'contains': ['360.a1.b1', '600.s1.b1', '720.g1.b1', '1200.g1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [2297, -1, 6979, -1, 4966, -1, 2346, -1], 'generators': [5791974151, 5313220382, 240], 'label': '21600.y.120.j1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '120.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947152
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.b1'], 'contains': ['240.d1.a1', '240.e1.b1', '240.f1.b1', '360.w1.a1', '360.x1.a1', '600.y1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7512, -1, 894, -1, 1540, -1, 3203, -1], 'generators': [43545600, 1963814094, 1959937465, 79843920, 39921960], 'label': '21600.y.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '120.k1.a1', 'projective_image': '21600.y', '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': '360.137'}
  • id: 63947153
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.a1'], 'contains': ['240.d1.b1', '240.e1.a1', '240.f1.a1', '360.w1.b1', '360.x1.b1', '600.y1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7512, -1, 4270, -1, 1540, -1, 1357, -1], 'generators': [2043377285, 43545600, 4877776404, 4837848924, 5792262062], 'label': '21600.y.120.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '120.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.b1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
  • id: 63947154
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.a1.b1', '36.a1.b1', '60.a1.b1', '60.c1.b1', '72.a1.b1', '120.b1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6222, -1, 4207, -1, 2833, -1, 1544, -1], 'generators': [39916800, 43545600, 5352848792, 80103271, 83472720], 'label': '21600.y.12.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '720.771'}
  • id: 63947155
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '60.e1.a1'], 'contains': ['360.y1.a1', '600.z1.a1', '720.o1.a1', '1200.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4961, -1, 9803, -1, 9721, -1, 2651, -1], 'generators': [5392767776, 43545600, 80086591], 'label': '21600.y.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.a1', 'old_label': '120.l1.a1', 'projective_image': '21600.y', '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': '120.35'}
  • id: 63947156
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '60.e1.b1'], 'contains': ['360.y1.b1', '600.z1.a2', '720.o1.b1', '1200.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4961, -1, 9662, -1, 9721, -1, 2761, -1], 'generators': [299674, 43545600, 2040079137], 'label': '21600.y.120.l1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.b1', 'old_label': '120.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947157
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.a1.b1', '72.b1.a1'], 'contains': ['288.a1.a1', '432.a1.a1', '720.b1.a1', '720.b1.b1', '720.c1.a1', '720.c1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9427, -1, 182, -1, 343, -1, 501, -1], 'generators': [39916800, 43545600, 5832178862, 12360], 'label': '21600.y.144.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947158
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '72.a1.a1', '72.c1.a1', '72.d1.a1'], 'contains': ['288.a1.a1', '432.b1.a1', '720.d1.a1', '720.f1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8443, -1, 2546, -1, 440, -1, 192, -1], 'generators': [43545600, 5792283806, 5792262062, 12360], 'label': '21600.y.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 63947159
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '72.a1.b1', '72.c1.b1', '72.d1.a1'], 'contains': ['288.a1.a1', '432.b1.b1', '720.d1.b1', '720.f1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8443, -1, 4897, -1, 440, -1, 23, -1], 'generators': [43545600, 2039748485, 5792262062, 12360], 'label': '21600.y.144.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.b1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 63947160
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.b1', '72.c1.a1', '72.f1.a1'], 'contains': ['288.a1.a1', '432.c1.a1', '720.i1.a1', '720.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8830, -1, 633, -1, 195, -1, 386, -1], 'generators': [2043377285, 43545600, 5792262062, 12360], 'label': '21600.y.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.c1.a1', 'projective_image': '21600.y', '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': '120.42'}
  • id: 63947161
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.c1.b1', '72.f1.a1'], 'contains': ['288.a1.a1', '432.c1.b1', '720.i1.b1', '720.m1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8830, -1, 355, -1, 195, -1, 334, -1], 'generators': [43545600, 5832200606, 5792262062, 12360], 'label': '21600.y.144.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 63947162
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.d1.a1', '72.f1.a1'], 'contains': ['288.a1.a1', '432.d1.a1', '720.n1.a1', '720.n1.b1', '720.o1.a1', '720.o1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9530, -1, 4465, -1, 786, -1, 552, -1], 'generators': [43545600, 4877785884, 5792262062, 12360], 'label': '21600.y.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.d1.a1', 'projective_image': '21600.y', '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': '200.49'}
  • id: 63947163
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.c1.a1', '72.c1.b1'], 'contains': ['288.a1.a1', '432.e1.a1', '720.q1.a1', '720.q1.b1', '720.r1.a1', '720.r1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9724, -1, 1227, -1, 700, -1, 457, -1], 'generators': [43545600, 5792262062, 4837869084, 12360], 'label': '21600.y.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.e1.a1', 'projective_image': '21600.y', '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': '600.174'}
  • id: 63947164
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '30.a1.a1', '50.a1.a1'], 'contains': ['300.a1.b1', '300.l1.b1', '300.r1.a1', '450.a1.a1', '450.b1.a1', '600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3371, -1, 7980, -1, 5906, -1, 7996, -1], 'generators': [3628800, 4834218540, 1963791510, 1959914882, 3927030, 4837852404], 'label': '21600.y.150.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '150.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947165
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1'], 'contains': ['24.a1.a1', '36.c1.a1', '60.f1.a1', '60.h1.a1', '72.c1.a1', '120.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7799, -1, 3662, -1, 2946, -1, 1812, -1], 'generators': [2043377285, 43545600, 4837858860, 5792262062, 4837849524], 'label': '21600.y.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.b1.a1', 'projective_image': '21600.y', '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': '3600.de'}
  • id: 63947166
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '30.a1.b1', '50.a1.b1'], 'contains': ['300.a1.a1', '300.l1.a1', '300.r1.b1', '450.a1.b1', '450.b1.b1', '600.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3371, -1, 6051, -1, 5906, -1, 8216, -1], 'generators': [5312972553, 2424, 1680, 5792221743, 83463240, 83462400], 'label': '21600.y.150.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.b1', 'old_label': '150.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.a1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947167
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.b1', '30.c1.a1', '50.a1.a1', '75.b1.b1'], 'contains': ['300.e1.b1', '300.j1.b1', '300.o1.a1', '450.a1.a1', '450.d1.a1', '600.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3934, -1, 7355, -1, 5632, -1, 4842, -1], 'generators': [39916800, 5356806064, 43545600, 1680, 5875397673, 5872097345], 'label': '21600.y.150.b1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '150.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947168
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '30.c1.b1', '50.a1.b1', '75.b1.a1'], 'contains': ['300.e1.a1', '300.j1.a1', '300.o1.b1', '450.a1.b1', '450.d1.b1', '600.c1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3934, -1, 4232, -1, 5632, -1, 5975, -1], 'generators': [39916800, 5356806064, 43545600, 2424, 1680, 83463240], 'label': '21600.y.150.b1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '150.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947169
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.b1', '50.a1.a1'], 'contains': ['300.c1.b1', '300.d1.b1', '300.g1.b1', '300.i1.b1', '300.m1.b1', '300.n1.b1', '300.p1.a1', '450.b1.a1', '450.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3088, -1, 7279, -1, 6598, -1, 6310, -1], 'generators': [4877764140, 39916800, 43545600, 4877774220, 1959914882, 4837852404], 'label': '21600.y.150.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '150.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 63947170
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.a1', '50.a1.b1'], 'contains': ['300.c1.a1', '300.d1.a1', '300.g1.a1', '300.i1.a1', '300.m1.a1', '300.n1.a1', '300.p1.b1', '450.b1.b1', '450.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3088, -1, 2545, -1, 6598, -1, 5487, -1], 'generators': [39916800, 5352890793, 43545600, 2424, 1680, 5792221743], 'label': '21600.y.150.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '150.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.c1.b1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 63947171
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '75.b1.b1'], 'contains': ['300.j1.b1', '300.o1.a1', '450.f1.a1', '450.g1.a1', '600.g1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2035, -1, 6567, -1, 6032, -1, 5006, -1], 'generators': [5356806064, 43545600, 39919224, 1680, 5831851137, 5872097345], 'label': '21600.y.150.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '150.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947172
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.b1', '75.b1.a1'], 'contains': ['300.j1.a1', '300.o1.b1', '450.f1.b1', '450.g1.b1', '600.g1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2035, -1, 7157, -1, 6032, -1, 6264, -1], 'generators': [5356806064, 43545600, 5832179105, 2424, 79834440, 1680], 'label': '21600.y.150.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '150.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.d1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947173
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.b1', '50.b1.a1', '75.b1.a1'], 'contains': ['300.o1.b1', '450.h1.a1', '450.i1.a1', '450.j1.b1', '600.n1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [959, -1, 8835, -1, 7472, -1, 6472, -1], 'generators': [5356806064, 43545600, 2424, 5792262305, 79834440, 1680], 'label': '21600.y.150.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.47'}
  • id: 63947174
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '50.b1.a1', '75.b1.b1'], 'contains': ['300.o1.a1', '450.h1.a1', '450.i1.b1', '450.j1.a1', '600.n1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [959, -1, 7211, -1, 7472, -1, 5612, -1], 'generators': [5791934337, 5356806064, 43545600, 2424, 1680, 5872097345], 'label': '21600.y.150.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.e1.b1', 'subgroup_fusion': None, 'weyl_group': '72.47'}
  • id: 63947175
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['50.b1.a1', '75.c1.a1'], 'contains': ['450.h1.a1', '450.k1.a1', '450.l1.a1', '600.p1.a1', '600.p1.b1', '600.z1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [659, -1, 9607, -1, 9582, -1, 6846, -1], 'generators': [5356806064, 43545600, 2424, 1680, 5791935177, 5872097345], 'label': '21600.y.150.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.f1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1029'}
  • id: 63947176
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.a1.b1', '36.c1.b1', '60.f1.b1', '60.h1.b1', '72.c1.b1', '120.e1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7799, -1, 4374, -1, 2946, -1, 1602, -1], 'generators': [43545600, 83732815, 79843920, 5312931992, 39921960], 'label': '21600.y.12.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '3600.de'}
  • id: 63947177
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['50.b1.a1', '75.c1.a2'], 'contains': ['450.h1.a1', '450.k1.a2', '450.l1.a2', '600.p1.a1', '600.p1.b1', '600.z1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [659, -1, 9743, -1, 9582, -1, 6751, -1], 'generators': [5356806064, 5871767337, 43545600, 2424, 1680, 5872097345], 'label': '21600.y.150.f1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.f1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.f1.a2', 'subgroup_fusion': None, 'weyl_group': '288.1029'}
  • id: 63947178
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.b1', '50.b1.a1'], 'contains': ['450.i1.a1', '450.j1.a1', '450.l1.a1', '450.l1.a2', '600.q1.b1', '600.r1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [157, -1, 9215, -1, 7610, -1, 5838, -1], 'generators': [840, 5871767337, 5313260464, 2424, 5792262305, 1680], 'label': '21600.y.150.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '150.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947179
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '50.b1.a1'], 'contains': ['450.i1.b1', '450.j1.b1', '450.l1.a1', '450.l1.a2', '600.q1.a1', '600.r1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [157, -1, 9700, -1, 7610, -1, 6555, -1], 'generators': [43546440, 5871767337, 5313260464, 2424, 1680, 5835807905], 'label': '21600.y.150.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '150.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.g1.b1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947180
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '30.g1.b1', '50.b1.a1', '75.a1.a1'], 'contains': ['450.i1.a1', '450.i1.b1', '450.k1.a1', '450.k1.a2', '600.s1.a1', '600.s1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [525, -1, 9266, -1, 7561, -1, 8262, -1], 'generators': [840, 5313260464, 2424, 5792262305, 5791933737, 1680], 'label': '21600.y.150.h1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947181
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['50.b1.a1'], 'contains': ['450.j1.a1', '450.j1.b1', '450.k1.a2', '450.l1.a1', '600.t1.a1', '600.t1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [236, -1, 9479, -1, 9500, -1, 5863, -1], 'generators': [43546440, 5313260464, 2424, 5791933737, 1680, 5835807905], 'label': '21600.y.150.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '150.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947182
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '150.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['50.b1.a1'], 'contains': ['450.j1.a1', '450.j1.b1', '450.k1.a1', '450.l1.a2', '600.t1.a1', '600.t1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [236, -1, 9558, -1, 9500, -1, 5812, -1], 'generators': [43546440, 5313260464, 2424, 5835479337, 1680, 5835807905], 'label': '21600.y.150.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '150.i1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.i1.a2', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947183
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.c1.a1', '90.a1.a1'], 'contains': ['360.o1.a1', '540.b1.a1', '720.a1.a1', '900.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5801, -1, 3576, -1, 3617, -1, 2299, -1], 'generators': [2424, 1680, 5875684380, 83463240, 83462400], 'label': '21600.y.180.a1.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.a1.a1', 'projective_image': '21600.y', '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': '24.13'}
  • id: 63947184
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.b1', '60.c1.b1', '90.a1.b1'], 'contains': ['360.o1.b1', '540.b1.b1', '720.a1.b1', '900.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5801, -1, 6344, -1, 3617, -1, 4198, -1], 'generators': [4834218540, 2043625110, 2043383282, 1959914882, 83462400], 'label': '21600.y.180.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.b1', 'old_label': '180.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947185
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '30.a1.a1', '60.d1.a1'], 'contains': ['360.b1.a1', '360.c1.b1', '360.d1.a1', '360.m1.a1', '360.r1.b1', '360.u1.a1', '360.w1.b1', '540.c1.a1', '900.e1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7726, -1, 3937, -1, 1960, -1, 2142, -1], 'generators': [3628800, 1963543685, 4834230804, 4837848924, 5795890862], 'label': '21600.y.180.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '180.b1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947186
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.a1.b1', '60.d1.b1'], 'contains': ['360.b1.b1', '360.c1.a1', '360.d1.b1', '360.m1.b1', '360.r1.a1', '360.u1.b1', '360.w1.a1', '540.c1.b1', '900.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7726, -1, 1660, -1, 1960, -1, 4053, -1], 'generators': [5160, 3628800, 3639120, 1963814094, 1959937465], 'label': '21600.y.180.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '180.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947187
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '6.b1.a1'], 'contains': ['24.a1.b1', '36.d1.a1', '60.g1.b1', '60.k1.a1', '72.d1.a1', '120.h1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2079, -1, 5406, -1, 3187, -1, 1477, -1], 'generators': [5160, 43545600, 80104015, 79843920, 5312931992], 'label': '21600.y.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1200.944'}
  • id: 63947188
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.a1.a1', '60.b1.a1', '90.b1.b1'], 'contains': ['360.a1.a1', '900.c1.a1', '1080.b1.a1', '1800.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5916, -1, 3783, -1, 3828, -1, 4366, -1], 'generators': [83473224, 6600, 83462400], 'label': '21600.y.180.c1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '180.c1.a1', 'projective_image': '21600.y', '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': '60.5'}
  • id: 63947189
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.b1', '60.a1.b1', '60.b1.b1', '90.b1.a1'], 'contains': ['360.a1.b1', '900.c1.b1', '1080.b1.b1', '1800.b1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5916, -1, 4163, -1, 3828, -1, 2425, -1], 'generators': [5875436311, 5396682542, 83462400], 'label': '21600.y.180.c1.b1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '180.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947190
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '60.e1.a1'], 'contains': ['360.y1.a1', '900.f1.a1', '1080.d1.a1', '1800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8588, -1, 7781, -1, 9456, -1, 2707, -1], 'generators': [39916800, 252991, 5312934176], 'label': '21600.y.180.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.a1', 'old_label': '180.d1.a1', 'projective_image': '21600.y', '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': '60.5'}
  • id: 63947191
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '60.e1.b1'], 'contains': ['360.y1.b1', '900.f1.a2', '1080.d1.b1', '1800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8588, -1, 7826, -1, 9456, -1, 2829, -1], 'generators': [39916800, 1960245537, 40216474], 'label': '21600.y.180.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.d1.b1', 'old_label': '180.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947192
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.a1'], 'contains': ['360.e1.a1', '360.g1.a1', '360.k1.a1', '360.l1.a1', '360.v1.b1', '360.v1.b2', '540.a1.a1', '900.g1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4418, -1, 3216, -1, 3084, -1, 1740, -1], 'generators': [39916800, 43545600, 4914094885, 1680, 5792223420], 'label': '21600.y.180.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '180.e1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947193
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.b1'], 'contains': ['360.e1.b1', '360.g1.b1', '360.k1.b1', '360.l1.b1', '360.v1.a1', '360.v1.a2', '540.a1.b1', '900.g1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4418, -1, 3366, -1, 3084, -1, 3639, -1], 'generators': [4877764140, 39916800, 43545600, 83468400, 5396700062], 'label': '21600.y.180.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '180.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947194
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '90.c1.a1'], 'contains': ['360.e1.a1', '360.i1.a1', '360.n1.a1', '540.b1.a1', '900.i1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5018, -1, 2278, -1, 4302, -1, 1869, -1], 'generators': [39916800, 43545600, 2424, 1680, 5792223420], 'label': '21600.y.180.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '180.f1.a1', 'projective_image': '21600.y', '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': '36.12'}
  • id: 63947195
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.b1', '90.c1.b1'], 'contains': ['360.e1.b1', '360.i1.b1', '360.n1.b1', '540.b1.b1', '900.i1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5018, -1, 7463, -1, 4302, -1, 3768, -1], 'generators': [4877764140, 39916800, 43545600, 2043383282, 1959914882], 'label': '21600.y.180.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '180.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.b1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 63947196
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '36.b1.a1', '60.d1.a1', '90.c1.a1'], 'contains': ['360.e1.a1', '360.f1.b1', '360.g1.a1', '360.j1.a1', '360.q1.b1', '360.t1.a1', '360.x1.b1', '540.c1.a1', '900.h1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7189, -1, 2395, -1, 2088, -1, 1528, -1], 'generators': [39916800, 43545600, 4914092461, 1680, 5792223420], 'label': '21600.y.180.g1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '180.g1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947197
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.b1', '36.b1.a1', '60.d1.b1', '90.c1.b1'], 'contains': ['360.e1.b1', '360.f1.a1', '360.g1.b1', '360.j1.b1', '360.q1.a1', '360.t1.b1', '360.x1.a1', '540.c1.b1', '900.h1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7189, -1, 1735, -1, 2088, -1, 3372, -1], 'generators': [4877764140, 39916800, 43545600, 4877781660, 83468400], 'label': '21600.y.180.g1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '180.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947198
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '6.b1.b1'], 'contains': ['24.a1.a1', '36.d1.b1', '60.g1.a1', '60.k1.b1', '72.d1.a1', '120.h1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2079, -1, 5174, -1, 3187, -1, 1740, -1], 'generators': [4877766324, 43545600, 2039748485, 5792262062, 4877775660], 'label': '21600.y.12.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '12.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1200.944'}
  • id: 63947199
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.a1'], 'contains': ['360.i1.a1', '360.j1.a1', '360.k1.a1', '360.v1.b1', '360.v1.b2', '360.x1.b1', '540.d1.a1', '900.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4527, -1, 2199, -1, 2956, -1, 1673, -1], 'generators': [43545600, 2424, 39918480, 4917721261, 5832140220], 'label': '21600.y.180.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '180.h1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947200
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.b1'], 'contains': ['360.i1.b1', '360.j1.b1', '360.k1.b1', '360.v1.a1', '360.v1.a2', '360.x1.a1', '540.d1.b1', '900.m1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4527, -1, 2062, -1, 2956, -1, 3572, -1], 'generators': [4877764140, 43545600, 2043383282, 1999831682, 5393071262], 'label': '21600.y.180.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '180.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947201
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.f1.a1', '90.a1.a1'], 'contains': ['360.o1.a1', '540.e1.a1', '720.l1.a1', '900.q1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6866, -1, 5118, -1, 3414, -1, 2252, -1], 'generators': [840, 2424, 1680, 4917721261, 5792221980], 'label': '21600.y.180.i1.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.i1.a1', 'projective_image': '21600.y', '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': '120.39'}
  • id: 63947202
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '60.f1.b1', '90.a1.b1'], 'contains': ['360.o1.b1', '540.e1.b1', '720.l1.b1', '900.q1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6866, -1, 6382, -1, 3414, -1, 4150, -1], 'generators': [4834218540, 1960162710, 1959914882, 5396700062, 1959920882], 'label': '21600.y.180.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.b1', 'old_label': '180.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.b1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 63947203
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '90.c1.a1'], 'contains': ['360.j1.a1', '360.l1.a1', '360.n1.a1', '540.e1.a1', '900.r1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5593, -1, 5027, -1, 3511, -1, 1803, -1], 'generators': [43545600, 2424, 1680, 4917721261, 5792223420], 'label': '21600.y.180.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '180.j1.a1', 'projective_image': '21600.y', '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': '180.26'}
  • id: 63947204
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.b1', '90.c1.b1'], 'contains': ['360.j1.b1', '360.l1.b1', '360.n1.b1', '540.e1.b1', '900.r1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5593, -1, 6951, -1, 3511, -1, 3702, -1], 'generators': [4877764140, 43545600, 2039754482, 1959914882, 5396700062], 'label': '21600.y.180.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '180.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1.b1', 'subgroup_fusion': None, 'weyl_group': '180.26'}
  • id: 63947205
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '90.c1.a1'], 'contains': ['360.i1.a1', '360.l1.a1', '360.q1.b1', '360.t1.a1', '360.v1.b1', '360.v1.b2', '540.f1.a1', '900.n1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4229, -1, 2604, -1, 3212, -1, 1607, -1], 'generators': [43545600, 4914092461, 2424, 39918480, 5832140220], 'label': '21600.y.180.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '180.k1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947206
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.b1', '90.c1.b1'], 'contains': ['360.i1.b1', '360.l1.b1', '360.q1.a1', '360.t1.b1', '360.v1.a1', '360.v1.a2', '540.f1.b1', '900.n1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4229, -1, 4976, -1, 3212, -1, 3438, -1], 'generators': [4877764140, 43545600, 2043383282, 1999831682, 5396700062], 'label': '21600.y.180.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '180.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947207
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '60.g1.a1', '90.c1.a1'], 'contains': ['360.k1.a1', '360.n1.a1', '360.t1.a1', '540.g1.a1', '900.v1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1922, -1, 5337, -1, 4521, -1, 1941, -1], 'generators': [43545600, 4914092461, 2424, 1680, 5792223420], 'label': '21600.y.180.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '180.l1.a1', 'projective_image': '21600.y', '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': '60.10'}
  • id: 63947208
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.b1', '60.g1.b1', '90.c1.b1'], 'contains': ['360.k1.b1', '360.n1.b1', '360.t1.b1', '540.g1.b1', '900.v1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1922, -1, 6616, -1, 4521, -1, 3839, -1], 'generators': [4877764140, 43545600, 2039754482, 5393071262, 1959914882], 'label': '21600.y.180.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '180.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.b1', 'subgroup_fusion': None, 'weyl_group': '60.10'}
  • id: 63947209
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.g1.a1', '45.a1.a1', '60.b1.b1', '75.a1.a1', '90.a1.a1', '150.a1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [3395, -1, 6022, -1, 5529, -1, 2782, -1], 'generators': [5791974151, 5313220382, 2424, 1680, 83463240, 83462400], 'label': '21600.y.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': '21600.y', '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': '720.768'}
  • id: 63947210
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '36.d1.b1', '60.g1.a1', '90.a1.a1'], 'contains': ['360.o1.a1', '540.g1.a1', '720.g1.b1', '900.w1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2012, -1, 5739, -1, 4416, -1, 2197, -1], 'generators': [4834258861, 840, 2424, 1680, 5792221980], 'label': '21600.y.180.m1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '180.m1.a1', 'projective_image': '21600.y', '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': '120.39'}
  • id: 63947211
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.b1', '36.d1.a1', '60.g1.b1', '90.a1.b1'], 'contains': ['360.o1.b1', '540.g1.b1', '720.g1.a1', '900.w1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2012, -1, 6432, -1, 4416, -1, 4107, -1], 'generators': [4834218540, 5313237662, 1960162710, 1959914882, 1959920882], 'label': '21600.y.180.m1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '180.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.m1.b1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 63947212
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '60.g1.a1'], 'contains': ['360.p1.a1', '540.g1.a1', '720.h1.b1', '900.x1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1158, -1, 6028, -1, 4627, -1, 1996, -1], 'generators': [5872055580, 4834258861, 2424, 79834440, 1680], 'label': '21600.y.180.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '180.n1.a1', 'projective_image': '21600.y', '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': '120.39'}
  • id: 63947213
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.b1', '60.g1.b1'], 'contains': ['360.p1.b1', '540.g1.b1', '720.h1.a1', '900.x1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1158, -1, 7590, -1, 4627, -1, 3894, -1], 'generators': [4834218540, 5313237662, 2003708310, 1959914882, 1959920882], 'label': '21600.y.180.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.b1', 'old_label': '180.n1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.n1.b1', 'subgroup_fusion': None, 'weyl_group': '120.39'}
  • id: 63947214
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.h1.a1', '60.i1.a1', '60.j1.a1', '90.b1.b1', '90.d1.b1'], 'contains': ['360.a1.a1', '900.q1.a1', '1080.j1.a1', '1800.r1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [5470, -1, 6836, -1, 4084, -1, 4324, -1], 'generators': [4837853940, 4837858164, 4837847340], 'label': '21600.y.180.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.b1', 'old_label': '180.o1.a1', 'projective_image': '21600.y', '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': '60.5'}
  • id: 63947215
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '60.h1.b1', '60.i1.b1', '60.j1.b1', '90.b1.a1', '90.d1.a1'], 'contains': ['360.a1.b1', '900.q1.b1', '1080.j1.b1', '1800.r1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 45, 'diagramx': [5470, -1, 4712, -1, 4084, -1, 2468, -1], 'generators': [5875437991, 5396684222, 83464080], 'label': '21600.y.180.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '180.o1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.o1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947216
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.k1.a1', '60.l1.a1', '90.b1.a1', '90.d1.a1', '90.e1.a1'], 'contains': ['360.a1.b1', '900.w1.a1', '1080.k1.a1', '1800.z1.a1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [1694, -1, 5614, -1, 4884, -1, 2522, -1], 'generators': [5791975591, 5313221822, 1680], 'label': '21600.y.180.p1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.p1.a1', 'projective_image': '21600.y', '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': '60.5'}
  • id: 63947217
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '180.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '60.k1.b1', '60.l1.b1', '90.b1.b1', '90.d1.b1', '90.e1.b1'], 'contains': ['360.a1.a1', '900.w1.b1', '1080.k1.b1', '1800.z1.b1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1694, -1, 8408, -1, 4884, -1, 4421, -1], 'generators': [4834218540, 4834225140, 4834229364], 'label': '21600.y.180.p1.b1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '180.p1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.p1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947218
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '50.a1.a1', '100.b1.a1'], 'contains': ['400.a1.a1', '400.b1.a1', '400.c1.b1', '600.a1.a1', '600.c1.a1', '600.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3462, -1, 5473, -1, 5077, -1, 5093, -1], 'generators': [39916800, 40204950, 43545600, 83467464, 40215030], 'label': '21600.y.200.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '200.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947219
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '50.a1.b1', '100.b1.a1'], 'contains': ['400.a1.a1', '400.b1.b1', '400.c1.a1', '600.a1.b1', '600.c1.b1', '600.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3462, -1, 6083, -1, 5077, -1, 4942, -1], 'generators': [39916800, 83462640, 43545600, 5792221743, 5392806153], 'label': '21600.y.200.a1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '200.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947220
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': ['10800.e1.a1', '10800.c1.b1', '10800.c1.a1', '10800.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '10.b1.a1', '10.b1.b1', '12.c1.a1', '12.c1.b1', '20.c1.a1', '20.c1.b1', '120.l1.a1', '120.l1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1882, 4160, 7876, 3247, 5623, 2509, 2667, 2279], 'generators': [305674, 43545600, 2003725593], 'label': '21600.y.2.a1.a1', 'mobius_quo': -1, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '120.a1.a1', '120.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '7200.cz'}
  • id: 63947221
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.b1'], 'contains': ['30.g1.b1', '45.a1.b1', '60.b1.a1', '75.a1.a1', '90.a1.b1', '150.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3395, -1, 7743, -1, 5529, -1, 4471, -1], 'generators': [4834218540, 5312938592, 2043625110, 5396693366, 1959914882, 83462400], 'label': '21600.y.15.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '15.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.b1', 'subgroup_fusion': None, 'weyl_group': '720.768'}
  • id: 63947222
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.b1.a1'], 'contains': ['400.a1.a1', '400.d1.a1', '400.e1.a1', '600.b1.a1', '600.e1.a1', '600.e1.b1', '600.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6615, -1, 6940, -1, 7873, -1, 5391, -1], 'generators': [39916800, 43545600, 15988, 83478384, 1959931561], 'label': '21600.y.200.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '200.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 63947223
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '100.b1.a1'], 'contains': ['400.b1.a1', '400.c1.a1', '400.e1.a1', '600.h1.a1', '600.k1.a1', '600.l1.a1', '600.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [5821, -1, 7118, -1, 5198, -1, 5144, -1], 'generators': [79849584, 43545600, 15988, 2043377281, 79850280], 'label': '21600.y.200.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '200.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.c1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 63947224
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.b1', '100.b1.a1'], 'contains': ['400.b1.b1', '400.c1.b1', '400.e1.a1', '600.h1.b1', '600.k1.b1', '600.l1.b1', '600.m1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [5821, -1, 7654, -1, 5198, -1, 4993, -1], 'generators': [83479080, 79849584, 2039748481, 43545600, 15988], 'label': '21600.y.200.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '200.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.c1.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 63947225
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '50.b1.a1', '100.a1.a1', '100.c1.a1', '100.d1.b1'], 'contains': ['600.n1.a1', '600.o1.a1', '600.p1.a1', '600.q1.a1', '600.r1.a1', '600.s1.a1', '600.t1.a1', '800.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1914, -1, 8755, -1, 7397, -1, 5714, -1], 'generators': [5871767337, 43545600, 2424, 79834440, 1680], 'label': '21600.y.200.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '200.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63947226
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '50.b1.a1', '100.a1.b1', '100.c1.b1', '100.d1.a1'], 'contains': ['600.n1.b1', '600.o1.b1', '600.p1.b1', '600.q1.b1', '600.r1.b1', '600.s1.b1', '600.t1.b1', '800.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1914, -1, 9421, -1, 7397, -1, 4541, -1], 'generators': [79833840, 5356806064, 5871767337, 43545600, 5792262305], 'label': '21600.y.200.d1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '200.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.d1.b1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 63947227
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '20.c1.b1', '100.b1.a1'], 'contains': ['400.b1.a1', '400.b1.b1', '400.d1.a1', '600.u1.a1', '600.u1.b1', '600.v1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3699, -1, 8636, -1, 6160, -1, 4893, -1], 'generators': [79849584, 2039748481, 43545600, 15988, 79850280], 'label': '21600.y.200.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '200.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947228
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '200.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.b1.a1'], 'contains': ['400.c1.a1', '400.c1.b1', '400.d1.a1', '600.x1.a1', '600.y1.a1', '600.y1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6376, -1, 6882, -1, 3979, -1, 5343, -1], 'generators': [83479080, 79849584, 43545600, 15988, 2043377281], 'label': '21600.y.200.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '200.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 63947229
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '72.a1.a1', '108.a1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.c1.b1', '1080.a1.a1', '1080.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9042, -1, 497, -1, 44, -1, 282, -1], 'generators': [39916800, 5832178862, 5832200606, 12360], 'label': '21600.y.216.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947230
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.b1', '72.a1.b1', '108.a1.a1'], 'contains': ['432.a1.a1', '432.b1.b1', '432.c1.a1', '1080.a1.b1', '1080.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9042, -1, 963, -1, 44, -1, 113, -1], 'generators': [2043377285, 5875724462, 12360, 83462400], 'label': '21600.y.216.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947231
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '108.a1.a1'], 'contains': ['432.a1.a1', '432.d1.a1', '432.e1.a1', '1080.c1.a1', '1080.c1.b1', '1080.d1.a1', '1080.d1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9664, -1, 3144, -1, 563, -1, 605, -1], 'generators': [3628800, 5795890862, 4837869084, 12360], 'label': '21600.y.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947232
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '15.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.c1.a1', '30.d1.a1', '30.e1.a1', '45.a1.a1', '75.b1.b1', '90.c1.a1', '150.c1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [3274, -1, 5093, -1, 5396, -1, 2701, -1], 'generators': [39916800, 43545600, 5396684222, 2424, 5835521191, 1680], 'label': '21600.y.15.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '15.b1.a1', 'projective_image': '21600.y', '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': '1080.492'}
  • id: 63947233
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '72.c1.a1', '108.a1.a1'], 'contains': ['432.b1.a1', '432.c1.a1', '432.e1.a1', '1080.f1.a1', '1080.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9200, -1, 1519, -1, 270, -1, 243, -1], 'generators': [1963543685, 5792262062, 4837869084, 12360], 'label': '21600.y.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947234
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '72.c1.b1', '108.a1.a1'], 'contains': ['432.b1.b1', '432.c1.b1', '432.e1.a1', '1080.f1.b1', '1080.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9200, -1, 1891, -1, 270, -1, 74, -1], 'generators': [1959914885, 5792262062, 4837869084, 12360], 'label': '21600.y.216.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.b1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947235
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.d1.b1', '72.d1.a1', '108.a1.a1'], 'contains': ['432.b1.a1', '432.b1.b1', '432.d1.a1', '1080.k1.a1', '1080.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8512, -1, 4702, -1, 638, -1, 153, -1], 'generators': [4834240284, 1959914885, 5792262062, 12360], 'label': '21600.y.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '216.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947236
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '108.a1.a1'], 'contains': ['432.c1.a1', '432.c1.b1', '432.d1.a1', '1080.m1.a1', '1080.m1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9348, -1, 772, -1, 119, -1, 425, -1], 'generators': [2043377285, 4834240284, 5792262062, 12360], 'label': '21600.y.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947237
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '225.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.b1', '75.a1.a1', '75.b1.a1'], 'contains': ['450.a1.b1', '450.f1.b1', '450.i1.a1', '675.a1.a1', '900.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1607, -1, 7704, -1, 6502, -1, 9005, -1], 'generators': [39916800, 5313260464, 5832179105, 2424, 1680, 39917640], 'label': '21600.y.225.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '225.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 63947238
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '225.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '75.a1.a1', '75.b1.b1'], 'contains': ['450.a1.a1', '450.f1.a1', '450.i1.b1', '675.a1.a1', '900.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1607, -1, 6598, -1, 6502, -1, 8134, -1], 'generators': [39916800, 5791934337, 5313260464, 5792263745, 2424, 1680], 'label': '21600.y.225.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '225.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.a1.b1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 63947239
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '225.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.a1.a1', '75.c1.a1'], 'contains': ['450.k1.a1', '675.a1.a1', '900.d1.a1', '900.d1.b1', '900.f1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1261, -1, 7837, -1, 9248, -1, 9609, -1], 'generators': [39916800, 5313260464, 5792263745, 2424, 1680, 5791935177], 'label': '21600.y.225.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '225.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947240
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '225.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.a1.a1', '75.c1.a2'], 'contains': ['450.k1.a2', '675.a1.a1', '900.d1.a1', '900.d1.b1', '900.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1261, -1, 7464, -1, 9248, -1, 9668, -1], 'generators': [5313260464, 5792263745, 5875396137, 2424, 1680, 83462400], 'label': '21600.y.225.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '225.b1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.b1.a2', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947241
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '225.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.b1.a1', '75.b1.b1', '75.c1.a1', '75.c1.a2'], 'contains': ['450.c1.a1', '450.d1.a1', '450.d1.b1', '450.e1.a1', '450.g1.a1', '450.g1.b1', '450.h1.a1', '675.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [910, -1, 6657, -1, 8792, -1, 7336, -1], 'generators': [39916800, 5356806064, 43545600, 2424, 1680, 5872097345], 'label': '21600.y.225.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '225.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.12'}
  • id: 63947242
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '120.b1.a1', '120.c1.b1', '120.d1.a1'], 'contains': ['480.a1.a1', '720.a1.a1', '720.b1.a1', '1200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7430, -1, 3707, -1, 1258, -1, 912, -1], 'generators': [39916800, 83462640, 43545600, 5875684380], 'label': '21600.y.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947243
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '15.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1'], 'contains': ['30.c1.b1', '30.d1.b1', '30.e1.b1', '45.a1.b1', '75.b1.a1', '90.c1.b1', '150.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3274, -1, 7417, -1, 5396, -1, 4340, -1], 'generators': [4877764140, 39916800, 5396689142, 43545600, 5396693366, 1959914882], 'label': '21600.y.15.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '15.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1080.492'}
  • id: 63947244
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.b1', '120.b1.b1', '120.c1.a1', '120.d1.b1'], 'contains': ['480.a1.b1', '720.a1.b1', '720.b1.b1', '1200.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7430, -1, 209, -1, 1258, -1, 2852, -1], 'generators': [39916800, 43545600, 1963791510, 83468400], 'label': '21600.y.240.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947245
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '120.b1.a1', '120.e1.a1', '120.h1.a1'], 'contains': ['480.a1.a1', '720.d1.a1', '720.e1.a1', '1200.e1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8278, -1, 3788, -1, 2590, -1, 669, -1], 'generators': [43545600, 5872097246, 5792274326, 5792262062], 'label': '21600.y.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947246
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '120.b1.b1', '120.e1.b1', '120.h1.b1'], 'contains': ['480.a1.b1', '720.d1.b1', '720.e1.b1', '1200.e1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8278, -1, 5001, -1, 2590, -1, 2687, -1], 'generators': [1959936721, 43545600, 2003730150, 79843920], 'label': '21600.y.240.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947247
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '60.g1.b1', '120.c1.a1', '120.g1.a1', '120.h1.b1'], 'contains': ['480.a1.b1', '720.f1.a1', '720.g1.a1', '720.h1.a1', '1200.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2584, -1, 2670, -1, 2438, -1, 2750, -1], 'generators': [43545600, 17520, 2003708310, 79839600], 'label': '21600.y.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.c1.a1', 'projective_image': '21600.y', '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': '40.13'}
  • id: 63947248
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '60.g1.a1', '120.c1.b1', '120.g1.b1', '120.h1.a1'], 'contains': ['480.a1.a1', '720.f1.b1', '720.g1.b1', '720.h1.b1', '1200.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2584, -1, 5765, -1, 2438, -1, 719, -1], 'generators': [5872055580, 79833840, 43545600, 4914092461], 'label': '21600.y.240.c1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.b1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 63947249
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.b1', '120.g1.a1', '120.k1.a1'], 'contains': ['480.a1.b1', '720.i1.a1', '720.j1.a1', '720.k1.a1', '1200.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7737, -1, 834, -1, 1462, -1, 2904, -1], 'generators': [1999853521, 43545600, 2003730150, 79843920], 'label': '21600.y.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.d1.a1', 'projective_image': '21600.y', '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': '72.46'}
  • id: 63947250
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '120.g1.b1', '120.k1.b1'], 'contains': ['480.a1.a1', '720.i1.b1', '720.j1.b1', '720.k1.b1', '1200.k1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7737, -1, 4301, -1, 1462, -1, 822, -1], 'generators': [43545600, 5832191126, 5872097246, 5792262062], 'label': '21600.y.240.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947251
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '120.c1.b1', '120.e1.a1', '120.k1.b1'], 'contains': ['480.a1.a1', '720.l1.a1', '720.m1.a1', '1200.h1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7514, -1, 4147, -1, 969, -1, 770, -1], 'generators': [5872055580, 79833840, 43545600, 4917721261], 'label': '21600.y.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.e1.a1', 'projective_image': '21600.y', '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': '120.42'}
  • id: 63947252
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.b1', '120.c1.a1', '120.e1.b1', '120.k1.a1'], 'contains': ['480.a1.b1', '720.l1.b1', '720.m1.b1', '1200.h1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7514, -1, 422, -1, 969, -1, 2800, -1], 'generators': [43545600, 2003708310, 79839600, 39934320], 'label': '21600.y.240.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 63947253
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.h1.a1', '120.k1.b1'], 'contains': ['480.a1.a1', '720.n1.a1', '720.p1.a1', '1200.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7883, -1, 4631, -1, 2711, -1, 963, -1], 'generators': [43545600, 5872097246, 4877776404, 5792262062], 'label': '21600.y.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.f1.a1', 'projective_image': '21600.y', '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': '120.42'}
  • id: 63947254
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '6.b1.a1'], 'contains': ['36.a1.b1', '36.c1.b1', '36.d1.a1', '90.a1.b1', '90.b1.a1', '108.a1.a1', '180.b1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [6089, -1, 4287, -1, 3059, -1, 1661, -1], 'generators': [5160, 39916800, 5352848792, 270415, 39927120], 'label': '21600.y.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '21600.y', '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': '600.146'}
  • id: 63947255
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '120.h1.b1', '120.k1.a1'], 'contains': ['480.a1.b1', '720.n1.b1', '720.p1.b1', '1200.l1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7883, -1, 3928, -1, 2711, -1, 2994, -1], 'generators': [43545600, 2003730150, 1959937465, 79843920], 'label': '21600.y.240.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 63947256
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.e1.a1', '120.g1.b1'], 'contains': ['480.a1.a1', '720.q1.a1', '720.s1.a1', '720.t1.b1', '1200.o1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8126, -1, 4233, -1, 2271, -1, 867, -1], 'generators': [43545600, 5872097246, 4837859604, 5792262062], 'label': '21600.y.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '240.g1.a1', 'projective_image': '21600.y', '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': '360.137'}
  • id: 63947257
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '120.e1.b1', '120.g1.a1'], 'contains': ['480.a1.b1', '720.q1.b1', '720.s1.b1', '720.t1.a1', '1200.o1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8126, -1, 1436, -1, 2271, -1, 2949, -1], 'generators': [43545600, 2003730150, 79843920, 1999854265], 'label': '21600.y.240.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '240.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.b1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
  • id: 63947258
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '270.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '90.a1.a1', '90.c1.a1'], 'contains': ['540.a1.a1', '540.b1.a1', '540.c1.a1', '540.d1.a1', '540.e1.a1', '540.f1.a1', '540.g1.a1', '1350.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4769, -1, 2925, -1, 3324, -1, 2581, -1], 'generators': [39916800, 4834258861, 2424, 1680, 5792223420], 'label': '21600.y.270.a1.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': '270.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.a1.a1', 'subgroup_fusion': None, 'weyl_group': '30.2'}
  • id: 63947259
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '270.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.b1', '90.a1.b1', '90.c1.b1'], 'contains': ['540.a1.b1', '540.b1.b1', '540.c1.b1', '540.d1.b1', '540.e1.b1', '540.f1.b1', '540.g1.b1', '1350.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4769, -1, 6263, -1, 3324, -1, 4480, -1], 'generators': [4834218540, 2043383282, 1959914882, 5396700062, 83462400], 'label': '21600.y.270.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.b1', 'old_label': '270.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.a1.b1', 'subgroup_fusion': None, 'weyl_group': '30.2'}
  • id: 63947260
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.b1.b1', '144.c1.a1', '144.c1.b1', '144.d1.a1', '144.e1.a1'], 'contains': ['864.a1.a1', '1440.a1.a1', '1440.a1.b1', '1440.b1.a1', '1440.b1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9479, -1, 253, -1, 653, -1, 526, -1], 'generators': [43545600, 5792262062, 12360], 'label': '21600.y.288.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '288.a1.a1', 'projective_image': '21600.y', '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': '8.5'}
  • id: 63947261
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '75.a1.a1', '100.a1.a1', '150.a1.b1'], 'contains': ['600.s1.a1', '900.b1.a1', '900.c1.a1', '900.d1.a1', '1200.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2601, -1, 6138, -1, 7077, -1, 8596, -1], 'generators': [5875396137, 2424, 1680, 83463240, 83462400], 'label': '21600.y.300.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.b1', 'old_label': '300.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947262
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.b1', '75.a1.a1', '100.a1.b1', '150.a1.a1'], 'contains': ['600.s1.b1', '900.b1.b1', '900.c1.b1', '900.d1.b1', '1200.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2601, -1, 8126, -1, 7077, -1, 8039, -1], 'generators': [83462640, 5313260464, 5875396137, 5875724705, 83462400], 'label': '21600.y.300.a1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '300.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947263
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.a1.b1', '100.b1.a1'], 'contains': ['600.a1.a1', '600.a1.b1', '600.b1.a1', '600.m1.a1', '600.m1.b1', '600.v1.a1', '600.x1.a1', '900.e1.a1', '900.e1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [6355, -1, 5954, -1, 5296, -1, 8335, -1], 'generators': [83479080, 15988, 2043377281, 83478384, 83462400], 'label': '21600.y.300.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '300.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947264
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.c1.b1'], 'contains': ['600.c1.a1', '600.e1.b1', '600.i1.a1', '600.j1.a1', '600.w1.b1', '600.w1.b2', '900.a1.a1', '900.g1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3035, -1, 2734, -1, 6793, -1, 5454, -1], 'generators': [39916800, 5352890793, 43545600, 5875686567, 1680], 'label': '21600.y.300.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '300.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947265
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '6.b1.b1'], 'contains': ['36.a1.a1', '36.c1.a1', '36.d1.b1', '90.a1.a1', '90.b1.b1', '108.a1.a1', '180.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6089, -1, 3952, -1, 3059, -1, 1937, -1], 'generators': [2043377285, 5875724462, 4834230060, 4834220724, 83462400], 'label': '21600.y.18.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '18.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
  • id: 63947266
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.c1.a1'], 'contains': ['600.c1.b1', '600.e1.a1', '600.i1.b1', '600.j1.b1', '600.w1.a1', '600.w1.a2', '900.a1.b1', '900.g1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3035, -1, 6974, -1, 6793, -1, 6232, -1], 'generators': [4877764140, 39916800, 43545600, 4877774220, 5396687606], 'label': '21600.y.300.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '300.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.c1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947267
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.b1.b1', '100.a1.a1', '150.c1.b1'], 'contains': ['600.c1.a1', '600.g1.a1', '600.n1.a1', '900.b1.a1', '900.i1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [2364, -1, 2386, -1, 6588, -1, 5656, -1], 'generators': [39916800, 5791934337, 43545600, 2424, 1680], 'label': '21600.y.300.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '300.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 63947268
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.b1.a1', '100.a1.b1', '150.c1.a1'], 'contains': ['600.c1.b1', '600.g1.b1', '600.n1.b1', '900.b1.b1', '900.i1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [2364, -1, 7928, -1, 6588, -1, 6476, -1], 'generators': [39916800, 5356806064, 83462640, 43545600, 5832179105], 'label': '21600.y.300.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '300.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.d1.b1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 63947269
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.c1.a1', '100.a1.a1', '150.b1.b1'], 'contains': ['600.o1.a1', '900.c1.a1', '900.i1.a1', '1200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5030, -1, 3677, -1, 5547, -1, 5912, -1], 'generators': [39916800, 43545600, 2424, 1680, 83463240], 'label': '21600.y.300.e1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '300.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947270
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.b1', '60.c1.b1', '100.a1.b1', '150.b1.a1'], 'contains': ['600.o1.b1', '900.c1.b1', '900.i1.b1', '1200.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5030, -1, 7680, -1, 5547, -1, 4587, -1], 'generators': [39916800, 5875395993, 5356806064, 5872095665, 43545600], 'label': '21600.y.300.e1.b1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '300.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.e1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947271
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.c1.a1', '75.c1.a2', '100.a1.a1'], 'contains': ['600.p1.a1', '900.d1.a1', '900.i1.a1', '1200.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1671, -1, 6888, -1, 9188, -1, 6869, -1], 'generators': [39916800, 43545600, 5875396137, 2424, 1680], 'label': '21600.y.300.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '300.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947272
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.c1.a1', '75.c1.a2', '100.a1.b1'], 'contains': ['600.p1.b1', '900.d1.b1', '900.i1.b1', '1200.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1671, -1, 8091, -1, 9188, -1, 6815, -1], 'generators': [39916800, 5356806064, 5872095665, 43545600, 5875396137], 'label': '21600.y.300.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.b1', 'old_label': '300.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.f1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947273
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '60.d1.b1', '100.b1.a1', '150.c1.b1'], 'contains': ['600.c1.a1', '600.d1.b1', '600.e1.b1', '600.h1.a1', '600.k1.b1', '600.u1.a1', '600.y1.b1', '900.e1.a1', '900.h1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6744, -1, 2164, -1, 5390, -1, 5044, -1], 'generators': [39916800, 5352890793, 43545600, 1680, 5792221743], 'label': '21600.y.300.g1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '300.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947274
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.b1', '60.d1.a1', '100.b1.a1', '150.c1.a1'], 'contains': ['600.c1.b1', '600.d1.a1', '600.e1.a1', '600.h1.b1', '600.k1.a1', '600.u1.b1', '600.y1.a1', '900.e1.b1', '900.h1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6744, -1, 4446, -1, 5390, -1, 6067, -1], 'generators': [4877764140, 39916800, 43545600, 4877774220, 4837852404], 'label': '21600.y.300.g1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '300.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.g1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947275
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '75.c1.a2'], 'contains': ['600.z1.a1', '900.f1.a1', '900.j1.a1', '1200.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4815, -1, 7215, -1, 9374, -1, 6682, -1], 'generators': [39916800, 5316890944, 43545600, 5875396137, 5872096409], 'label': '21600.y.300.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a1', 'old_label': '300.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947276
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1', '10.a1.b1'], 'contains': ['40.a1.a1', '60.a1.a1', '60.b1.a1', '100.a1.a1', '120.c1.a1', '200.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4997, -1, 5335, -1, 4968, -1, 4059, -1], 'generators': [39916800, 43545600, 5352848792, 5392772192, 83473224], 'label': '21600.y.20.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '20.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '720.771'}
  • id: 63947277
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.b1', '75.c1.a1'], 'contains': ['600.z1.a2', '900.f1.a2', '900.j1.a2', '1200.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4815, -1, 7845, -1, 9374, -1, 6749, -1], 'generators': [39916800, 5316890944, 43545600, 5832181289, 5791935177], 'label': '21600.y.300.h1.a2', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a2', 'old_label': '300.h1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.a2', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947278
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.c1.b1'], 'contains': ['600.g1.a1', '600.h1.a1', '600.i1.a1', '600.w1.b1', '600.w1.b2', '600.y1.b1', '900.l1.a1', '900.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2466, -1, 2095, -1, 6278, -1, 5503, -1], 'generators': [5352890793, 43545600, 5832138543, 2424, 39918480], 'label': '21600.y.300.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '300.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947279
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.c1.a1'], 'contains': ['600.g1.b1', '600.h1.b1', '600.i1.b1', '600.w1.a1', '600.w1.a2', '600.y1.a1', '900.l1.b1', '900.m1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2466, -1, 7273, -1, 6278, -1, 6281, -1], 'generators': [4877769204, 43545600, 4837857420, 1959914882, 4837847340], 'label': '21600.y.300.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '300.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.i1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947280
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.h1.a1', '100.c1.a1', '150.b1.b1', '150.d1.b1'], 'contains': ['600.o1.a1', '900.q1.a1', '900.r1.a1', '1200.h1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4070, -1, 6627, -1, 5710, -1, 5954, -1], 'generators': [43545600, 2424, 79834440, 1680, 5316889264], 'label': '21600.y.300.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '300.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947281
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.b1', '60.h1.b1', '100.c1.b1', '150.b1.a1', '150.d1.a1'], 'contains': ['600.o1.b1', '900.q1.b1', '900.r1.b1', '1200.h1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4070, -1, 8170, -1, 5710, -1, 4630, -1], 'generators': [5356806064, 5875726145, 43545600, 39918480, 5875397673], 'label': '21600.y.300.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '300.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.j1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947282
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.a1', '100.c1.a1'], 'contains': ['600.r1.a1', '900.q1.a1', '900.t1.a1', '1200.i1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4219, -1, 6824, -1, 5628, -1, 5845, -1], 'generators': [840, 5832138543, 2424, 1680, 5392806153], 'label': '21600.y.300.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.k1.a1', 'old_label': '300.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947283
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.b1', '100.c1.b1'], 'contains': ['600.r1.b1', '900.q1.b1', '900.t1.b1', '1200.i1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4219, -1, 8449, -1, 5628, -1, 6604, -1], 'generators': [43843830, 4834218540, 1960162710, 1959914882, 4837852404], 'label': '21600.y.300.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.k1.b1', 'old_label': '300.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.k1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947284
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.a1', '100.c1.a1', '150.a1.b1'], 'contains': ['600.s1.a1', '900.q1.a1', '900.s1.a1', '1200.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3566, -1, 6671, -1, 5955, -1, 8553, -1], 'generators': [840, 5312972553, 5832138543, 2424, 1680], 'label': '21600.y.300.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.b1', 'old_label': '300.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947285
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.b1', '100.c1.b1', '150.a1.a1'], 'contains': ['600.s1.b1', '900.q1.b1', '900.s1.b1', '1200.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3566, -1, 8362, -1, 5955, -1, 7996, -1], 'generators': [298230, 4834218540, 1960162710, 1959914882, 4837852404], 'label': '21600.y.300.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '300.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.l1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947286
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.c1.a1', '150.c1.b1'], 'contains': ['600.h1.a1', '600.j1.a1', '600.n1.a1', '900.r1.a1', '900.s1.a1', '900.t1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3305, -1, 5771, -1, 6980, -1, 5593, -1], 'generators': [5312973993, 43545600, 5832138543, 2424, 1680], 'label': '21600.y.300.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '300.m1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.m1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 63947287
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.a1.a1'], 'contains': ['40.a1.b1', '60.a1.b1', '60.b1.b1', '100.a1.b1', '120.c1.b1', '200.a1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [4997, -1, 6056, -1, 4968, -1, 2335, -1], 'generators': [39916800, 83462640, 5313220382, 43545600, 5835519751], 'label': '21600.y.20.a1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.b1', 'subgroup_fusion': None, 'weyl_group': '720.771'}
  • id: 63947288
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.c1.b1', '150.c1.a1'], 'contains': ['600.h1.b1', '600.j1.b1', '600.n1.b1', '900.r1.b1', '900.s1.b1', '900.t1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3305, -1, 8769, -1, 6980, -1, 6413, -1], 'generators': [4877764140, 43545600, 4877774220, 1959914882, 4837852404], 'label': '21600.y.300.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '300.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.m1.b1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 63947289
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.a1', '150.c1.b1'], 'contains': ['600.g1.a1', '600.j1.a1', '600.k1.b1', '600.u1.a1', '600.w1.b1', '600.w1.b2', '900.n1.b1', '900.u1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2697, -1, 2522, -1, 6372, -1, 5195, -1], 'generators': [5352890793, 43545600, 2424, 39918480, 5792221743], 'label': '21600.y.300.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '300.n1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947290
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.d1.b1', '150.c1.a1'], 'contains': ['600.g1.b1', '600.j1.b1', '600.k1.a1', '600.u1.b1', '600.w1.a1', '600.w1.a2', '900.n1.a1', '900.u1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2697, -1, 7351, -1, 6372, -1, 6182, -1], 'generators': [43545600, 4837857420, 1959914882, 4837847340, 4837852404], 'label': '21600.y.300.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '300.n1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.n1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947502
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.a1', '144.d1.a1', '360.h1.a1'], 'contains': ['1440.b1.a1', '2160.h1.a1', '3600.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9906, -1, 4830, -1, 3989, -1, 2505, -1], 'generators': [43545600, 4877785884, 4913776353], 'label': '21600.y.720.o1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.a1', 'old_label': '720.o1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947291
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.g1.b1', '60.k1.a1', '100.d1.a1', '150.b1.a1', '150.d1.a1', '150.e1.b1'], 'contains': ['600.o1.b1', '900.v1.a1', '900.w1.a1', '900.x1.a1', '1200.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1343, -1, 7526, -1, 6882, -1, 4672, -1], 'generators': [5356806064, 43545600, 1680, 5871768873, 5872097345], 'label': '21600.y.300.o1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '300.o1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947292
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.g1.a1', '60.k1.b1', '100.d1.b1', '150.b1.b1', '150.d1.b1', '150.e1.a1'], 'contains': ['600.o1.a1', '900.v1.b1', '900.w1.b1', '900.x1.b1', '1200.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1343, -1, 8514, -1, 6882, -1, 5996, -1], 'generators': [5356806064, 43545600, 2424, 79834440, 1680], 'label': '21600.y.300.o1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '300.o1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.o1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947293
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.b1', '100.d1.a1', '150.c1.a1'], 'contains': ['600.i1.b1', '600.n1.b1', '600.u1.b1', '900.v1.a1', '900.y1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1153, -1, 8957, -1, 7205, -1, 6339, -1], 'generators': [4877764140, 4877769204, 43545600, 4877774220, 1959914882], 'label': '21600.y.300.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '300.p1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.p1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 63947294
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '100.d1.b1', '150.c1.b1'], 'contains': ['600.i1.a1', '600.n1.a1', '600.u1.a1', '900.v1.b1', '900.y1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1153, -1, 5152, -1, 7205, -1, 5253, -1], 'generators': [5312973993, 43545600, 2424, 1680, 5792221743], 'label': '21600.y.300.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '300.p1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.p1.b1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 63947295
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.b1', '100.d1.a1'], 'contains': ['600.q1.b1', '900.x1.a1', '900.y1.a1', '1200.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [356, -1, 8903, -1, 7309, -1, 4763, -1], 'generators': [43843830, 4834218540, 4834223604, 2003708310, 1959914882], 'label': '21600.y.300.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.d1.a1', 'old_label': '300.q1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.q1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947296
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '100.d1.b1'], 'contains': ['600.q1.a1', '900.x1.b1', '900.y1.b1', '1200.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [356, -1, 9189, -1, 7309, -1, 6112, -1], 'generators': [2424, 79834440, 1680, 5792221743, 5392806153], 'label': '21600.y.300.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.d1.b1', 'old_label': '300.q1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.q1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947297
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.b1', '60.l1.a1', '100.d1.a1', '150.a1.a1'], 'contains': ['600.s1.b1', '900.w1.a1', '900.y1.a1', '1200.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1024, -1, 9032, -1, 6460, -1, 7918, -1], 'generators': [298230, 4834218540, 4834223604, 1960162710, 1959914882], 'label': '21600.y.300.r1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '300.r1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.r1.a1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947298
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.b1'], 'contains': ['40.a1.a1', '60.h1.a1', '60.i1.a1', '60.j1.a1', '100.c1.a1', '120.g1.a1', '200.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5394, -1, 6807, -1, 4855, -1, 4000, -1], 'generators': [43545600, 5832138543, 1584, 80081432, 79855344], 'label': '21600.y.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '20.b1.a1', 'projective_image': '21600.y', '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': '2160.cm'}
  • id: 63947299
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '300.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '60.l1.b1', '100.d1.b1', '150.a1.b1'], 'contains': ['600.s1.a1', '900.w1.b1', '900.y1.b1', '1200.g1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1024, -1, 8548, -1, 6460, -1, 8180, -1], 'generators': [840, 5312972553, 2424, 1680, 5792221743], 'label': '21600.y.300.r1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '300.r1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.r1.b1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
  • id: 63947300
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.b1', 'complements': ['60.e1.a1', '60.e1.b1', '60.a1.b1', '60.h1.b1', '60.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.a1.a1', '120.i1.a1', '120.j1.a1', '180.c1.a1', '180.o1.a1', '180.p1.b1'], 'contains': ['1800.u1.a1', '2160.d1.a1', '3600.g1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5328, 2659, 8358, 3933, 4611, 3927, 4107, 4639], 'generators': [10824, 6600], 'label': '21600.y.360.a1.a1', 'mobius_quo': -1, 'mobius_sub': -180, 'normal_closure': '360.a1.a1', 'normal_contained_in': ['6.a1.a1', '120.a1.a1'], 'normal_contains': ['21600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': '60.5', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947301
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.a1', 'complements': ['60.e1.b1', '60.e1.a1', '60.a1.a1', '60.h1.a1', '60.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '120.a1.b1', '120.i1.b1', '120.j1.b1', '180.c1.b1', '180.o1.b1', '180.p1.a1'], 'contains': ['1800.u1.b1', '2160.d1.b1', '3600.g1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5328, 2659, 6195, 2169, 4611, 3927, 2076, 2990], 'generators': [5313220142, 5791973911], 'label': '21600.y.360.a1.b1', 'mobius_quo': -1, 'mobius_sub': -180, 'normal_closure': '360.a1.b1', 'normal_contained_in': ['6.a1.a1', '120.a1.b1'], 'normal_contains': ['21600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '360.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': '60.5', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '360.a1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947302
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '120.b1.a1', '180.b1.a1'], 'contains': ['720.a1.a1', '720.e1.a1', '720.j1.b1', '1080.a1.a1', '1800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8422, -1, 3774, -1, 1562, -1, 1759, -1], 'generators': [39916800, 5832191126, 5832178862, 5792263646], 'label': '21600.y.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.b1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947303
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.b1', '120.b1.b1', '180.b1.b1'], 'contains': ['720.a1.b1', '720.e1.b1', '720.j1.a1', '1080.a1.b1', '1800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8422, -1, 908, -1, 1562, -1, 3778, -1], 'generators': [1959936721, 3628800, 3639120, 1963813350], 'label': '21600.y.360.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '360.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947304
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '90.a1.b1', '120.c1.a1', '180.b1.b1'], 'contains': ['720.a1.b1', '720.g1.a1', '720.l1.b1', '1080.b1.a1', '1800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [5254, -1, 676, -1, 1061, -1, 3947, -1], 'generators': [2043625110, 17520, 83468400, 83462400], 'label': '21600.y.360.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '360.c1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947305
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.b1', '90.a1.a1', '120.c1.b1', '180.b1.a1'], 'contains': ['720.a1.a1', '720.g1.b1', '720.l1.a1', '1080.b1.b1', '1800.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [5254, -1, 3863, -1, 1061, -1, 1960, -1], 'generators': [4834258861, 83462640, 5875684380, 83462400], 'label': '21600.y.360.c1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947306
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '180.b1.a1'], 'contains': ['720.a1.a1', '720.p1.a1', '720.s1.a1', '1080.c1.a1', '1800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8770, -1, 3902, -1, 2208, -1, 2051, -1], 'generators': [39916800, 5832178862, 4834230804, 5792263646], 'label': '21600.y.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.d1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947307
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '180.b1.b1'], 'contains': ['720.a1.b1', '720.p1.b1', '720.s1.b1', '1080.c1.b1', '1800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8770, -1, 3177, -1, 2208, -1, 4081, -1], 'generators': [3628800, 3639120, 1963813350, 1959937465], 'label': '21600.y.360.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '360.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947308
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.b1.a1', '180.e1.a1', '180.f1.a1', '180.g1.a1'], 'contains': ['720.b1.a1', '720.d1.a1', '720.i1.b1', '1080.a1.a1', '1800.e1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7269, -1, 773, -1, 1660, -1, 1227, -1], 'generators': [39916800, 43545600, 1680, 5792223420], 'label': '21600.y.360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.e1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947309
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['40.a1.b1', '60.h1.b1', '60.i1.b1', '60.j1.b1', '100.c1.b1', '120.g1.b1', '200.c1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [5394, -1, 7523, -1, 4855, -1, 2276, -1], 'generators': [2039769482, 83479080, 79849584, 43545600, 304137], 'label': '21600.y.20.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2160.cm'}
  • id: 63947310
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.b1', '120.b1.b1', '180.e1.b1', '180.f1.b1', '180.g1.b1'], 'contains': ['720.b1.b1', '720.d1.b1', '720.i1.a1', '1080.a1.b1', '1800.e1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7269, -1, 1091, -1, 1660, -1, 3258, -1], 'generators': [4877764140, 39916800, 43545600, 83468400], 'label': '21600.y.360.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947311
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '72.a1.a1', '120.c1.a1', '180.g1.b1'], 'contains': ['720.b1.b1', '720.f1.a1', '720.m1.b1', '1080.b1.a1', '1800.e1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7137, -1, 571, -1, 879, -1, 3096, -1], 'generators': [39916800, 43545600, 17520, 83468400], 'label': '21600.y.360.f1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '360.f1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947312
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.b1', '72.a1.b1', '120.c1.b1', '180.g1.a1'], 'contains': ['720.b1.a1', '720.f1.b1', '720.m1.a1', '1080.b1.b1', '1800.e1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7137, -1, 1129, -1, 879, -1, 1023, -1], 'generators': [39916800, 43545600, 4914092461, 5792221740], 'label': '21600.y.360.f1.b1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '360.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947313
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '120.d1.a1', '180.e1.a1', '180.g1.a1'], 'contains': ['720.b1.a1', '720.n1.a1', '720.q1.a1', '1080.c1.a1', '1800.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8499, -1, 3134, -1, 2349, -1, 1152, -1], 'generators': [39916800, 43545600, 4914094141, 5792221740], 'label': '21600.y.360.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.g1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947314
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '120.d1.b1', '180.e1.b1', '180.g1.b1'], 'contains': ['720.b1.b1', '720.n1.b1', '720.q1.b1', '1080.c1.b1', '1800.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8499, -1, 3206, -1, 2349, -1, 3182, -1], 'generators': [39916800, 43545600, 83468400, 5396700062], 'label': '21600.y.360.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947315
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '72.b1.a1'], 'contains': ['720.c1.a1', '720.o1.a1', '720.r1.a1', '1080.d1.a1', '1800.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9873, -1, 2995, -1, 3920, -1, 2503, -1], 'generators': [39916800, 43545600, 4913776353, 4837869084], 'label': '21600.y.360.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.a1', 'old_label': '360.h1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947316
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.b1', '72.b1.a1'], 'contains': ['720.c1.b1', '720.o1.b1', '720.r1.b1', '1080.d1.b1', '1800.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9873, -1, 3383, -1, 3920, -1, 2570, -1], 'generators': [39916800, 43545600, 5832191222, 4837869084], 'label': '21600.y.360.h1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.b1', 'old_label': '360.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947317
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.a1', '180.h1.a1', '180.k1.a1'], 'contains': ['720.d1.a1', '720.i1.b1', '1080.e1.a1', '1800.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4619, -1, 2193, -1, 3201, -1, 1408, -1], 'generators': [43545600, 2424, 39918480, 5832140220], 'label': '21600.y.360.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.i1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947318
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.b1', '180.h1.b1', '180.k1.b1'], 'contains': ['720.d1.b1', '720.i1.a1', '1080.e1.b1', '1800.k1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4619, -1, 5517, -1, 3201, -1, 3438, -1], 'generators': [4877764140, 43545600, 2043383282, 1999831682], 'label': '21600.y.360.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947319
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '120.e1.a1', '180.g1.a1', '180.h1.a1', '180.j1.a1'], 'contains': ['720.d1.a1', '720.m1.a1', '720.q1.a1', '1080.f1.a1', '1800.h1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7513, -1, 2287, -1, 2513, -1, 1188, -1], 'generators': [43545600, 1680, 4917721261, 5792223420], 'label': '21600.y.360.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.j1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947320
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '10.a1.a1'], 'contains': ['40.a1.b1', '60.k1.a1', '60.l1.a1', '100.d1.a1', '120.h1.a1', '200.e1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [1879, -1, 7694, -1, 5268, -1, 2217, -1], 'generators': [2039769482, 79849584, 43545600, 304137, 79850280], 'label': '21600.y.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '21600.y', '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': '720.771'}
  • id: 63947321
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '120.e1.b1', '180.g1.b1', '180.h1.b1', '180.j1.b1'], 'contains': ['720.d1.b1', '720.m1.b1', '720.q1.b1', '1080.f1.b1', '1800.h1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7513, -1, 1678, -1, 2513, -1, 3218, -1], 'generators': [4877764140, 43545600, 79839600, 4837864860], 'label': '21600.y.360.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947322
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '180.h1.a1', '180.l1.a1'], 'contains': ['720.d1.a1', '720.n1.a1', '1080.g1.a1', '1800.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4391, -1, 4602, -1, 3630, -1, 1484, -1], 'generators': [43545600, 4914094885, 1680, 5792223420], 'label': '21600.y.360.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.k1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947323
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.b1', '180.h1.b1', '180.l1.b1'], 'contains': ['720.d1.b1', '720.n1.b1', '1080.g1.b1', '1800.l1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4391, -1, 5602, -1, 3630, -1, 3514, -1], 'generators': [4877764140, 43545600, 5393071262, 79839600], 'label': '21600.y.360.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947324
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '180.j1.a1', '180.k1.a1'], 'contains': ['720.d1.a1', '720.q1.a1', '1080.h1.a1', '1800.n1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4274, -1, 3264, -1, 3373, -1, 1448, -1], 'generators': [43545600, 4917723685, 1680, 5792223420], 'label': '21600.y.360.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.l1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947325
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.b1', '180.j1.b1', '180.k1.b1'], 'contains': ['720.d1.b1', '720.q1.b1', '1080.h1.b1', '1800.n1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4274, -1, 5573, -1, 3373, -1, 3478, -1], 'generators': [4877764140, 43545600, 79839600, 5396700062], 'label': '21600.y.360.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947326
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '120.e1.a1', '180.b1.a1'], 'contains': ['720.e1.a1', '720.l1.a1', '720.s1.a1', '1080.f1.a1', '1800.r1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8917, -1, 3823, -1, 2034, -1, 1712, -1], 'generators': [1963543685, 4837859604, 4837848924, 5792262062], 'label': '21600.y.360.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.m1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947327
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '120.e1.b1', '180.b1.b1'], 'contains': ['720.e1.b1', '720.l1.b1', '720.s1.b1', '1080.f1.b1', '1800.r1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8917, -1, 1629, -1, 2034, -1, 3731, -1], 'generators': [10320, 1999854265, 2000102094, 39921960], 'label': '21600.y.360.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '360.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.m1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947328
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.a1', '180.f1.a1', '180.j1.a1', '180.l1.a1'], 'contains': ['720.d1.a1', '1080.i1.a1', '1800.s1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5432, -1, 5701, -1, 4093, -1, 1531, -1], 'generators': [43545600, 2424, 1680, 5792223420], 'label': '21600.y.360.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '360.n1.a1', 'projective_image': '21600.y', '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': '12.5'}
  • id: 63947329
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.b1', '180.f1.b1', '180.j1.b1', '180.l1.b1'], 'contains': ['720.d1.b1', '1080.i1.b1', '1800.s1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5432, -1, 7508, -1, 4093, -1, 3562, -1], 'generators': [4877764140, 43545600, 2039754482, 1959914882], 'label': '21600.y.360.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '360.n1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 63947330
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '120.f1.a1', '180.a1.a1', '180.i1.a1', '180.m1.a1'], 'contains': ['1080.i1.a1', '1440.c1.a1', '1800.u1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7047, -1, 5749, -1, 4003, -1, 1850, -1], 'generators': [840, 2424, 1680, 5792221980], 'label': '21600.y.360.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '360.o1.a1', 'projective_image': '21600.y', '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': '24.13'}
  • id: 63947331
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '15.a1.a1', '15.a1.b1', '18.a1.a1', '18.a1.b1', '30.a1.a1', '30.a1.b1', '180.d1.a1', '180.d1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5482, -1, 6041, -1, 5421, -1, 2732, -1], 'generators': [39916800, 40222474, 2000096793], 'label': '21600.y.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': '21600.y', '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': '3600.a'}
  • id: 63947332
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '10.a1.b1'], 'contains': ['40.a1.a1', '60.k1.b1', '60.l1.b1', '100.d1.b1', '120.h1.b1', '200.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1879, -1, 8283, -1, 5268, -1, 3941, -1], 'generators': [43545600, 1584, 80081432, 5792221743, 79855344], 'label': '21600.y.20.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '20.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.b1', 'subgroup_fusion': None, 'weyl_group': '720.771'}
  • id: 63947333
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '120.f1.b1', '180.a1.b1', '180.i1.b1', '180.m1.b1'], 'contains': ['1080.i1.b1', '1440.c1.b1', '1800.u1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7047, -1, 6377, -1, 4003, -1, 3880, -1], 'generators': [4834218540, 1960162710, 1959914882, 1959920882], 'label': '21600.y.360.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '360.o1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.o1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947334
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.a1', '180.n1.a1'], 'contains': ['1080.i1.a1', '1440.d1.b1', '1800.w1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4097, -1, 5921, -1, 4184, -1, 1578, -1], 'generators': [5872055580, 2424, 79834440, 1680], 'label': '21600.y.360.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '360.p1.a1', 'projective_image': '21600.y', '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': '24.13'}
  • id: 63947335
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.b1', '180.n1.b1'], 'contains': ['1080.i1.b1', '1440.d1.a1', '1800.w1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4097, -1, 7645, -1, 4184, -1, 3609, -1], 'generators': [4834218540, 2003708310, 1959914882, 1959920882], 'label': '21600.y.360.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.b1', 'old_label': '360.p1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947336
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.a1', '72.c1.a1', '120.g1.a1', '180.g1.b1', '180.k1.b1'], 'contains': ['720.f1.a1', '720.i1.a1', '720.q1.b1', '1080.j1.a1', '1800.h1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6219, -1, 1575, -1, 1929, -1, 3041, -1], 'generators': [43545600, 79839600, 4837864860, 4837847340], 'label': '21600.y.360.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.q1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947337
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.b1', '72.c1.b1', '120.g1.b1', '180.g1.a1', '180.k1.a1'], 'contains': ['720.f1.b1', '720.i1.b1', '720.q1.a1', '1080.j1.b1', '1800.h1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6219, -1, 2588, -1, 1929, -1, 1066, -1], 'generators': [43545600, 4914092461, 39918480, 5832140220], 'label': '21600.y.360.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.q1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.q1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947338
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.a1', '120.g1.a1', '180.b1.b1'], 'contains': ['720.g1.a1', '720.j1.a1', '720.s1.b1', '1080.j1.a1', '1800.i1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [6290, -1, 1410, -1, 1846, -1, 4045, -1], 'generators': [5160, 10320, 1960185294, 1999854265], 'label': '21600.y.360.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '360.r1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947339
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.b1', '120.g1.b1', '180.b1.a1'], 'contains': ['720.g1.b1', '720.j1.b1', '720.s1.a1', '1080.j1.b1', '1800.i1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [6290, -1, 4137, -1, 1846, -1, 1917, -1], 'generators': [1959914885, 4837859604, 5792262062, 4834220124], 'label': '21600.y.360.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.r1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.r1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947340
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.a1', '120.g1.a1'], 'contains': ['720.h1.a1', '720.k1.a1', '720.t1.a1', '1080.j1.a1', '1800.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6002, -1, 3608, -1, 2140, -1, 3688, -1], 'generators': [5160, 10320, 1999854265, 2003730894], 'label': '21600.y.360.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.s1.a1', 'old_label': '360.s1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947341
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.b1', '120.g1.b1'], 'contains': ['720.h1.b1', '720.k1.b1', '720.t1.b1', '1080.j1.b1', '1800.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6002, -1, 5149, -1, 2140, -1, 1657, -1], 'generators': [1959914885, 4837859604, 5792262062, 4877765724], 'label': '21600.y.360.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.s1.b1', 'old_label': '360.s1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.s1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947342
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '72.d1.a1', '120.h1.a1', '180.g1.a1', '180.k1.a1', '180.l1.a1'], 'contains': ['720.d1.a1', '720.f1.b1', '720.n1.a1', '1080.k1.a1', '1800.q1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2842, -1, 5203, -1, 3014, -1, 1275, -1], 'generators': [43545600, 4914092461, 1680, 5792223420], 'label': '21600.y.360.t1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.t1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947343
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.c1.b1'], 'contains': ['72.e1.a1', '120.a1.a1', '120.f1.a1', '144.b1.a1', '240.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6222, -1, 3629, -1, 2992, -1, 1560, -1], 'generators': [5872107182, 5872097846, 43545600, 5792262062], 'label': '21600.y.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '24.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '240.190'}
  • id: 63947344
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.b1', '72.d1.a1', '120.h1.b1', '180.g1.b1', '180.k1.b1', '180.l1.b1'], 'contains': ['720.d1.b1', '720.f1.a1', '720.n1.b1', '1080.k1.b1', '1800.q1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2842, -1, 4841, -1, 3014, -1, 3305, -1], 'generators': [4877764140, 43545600, 4877781660, 79839600], 'label': '21600.y.360.t1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.t1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.t1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947345
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '60.l1.a1', '120.h1.a1', '180.b1.a1'], 'contains': ['720.e1.a1', '720.g1.b1', '720.p1.a1', '1080.k1.a1', '1800.z1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2074, -1, 5318, -1, 2848, -1, 1807, -1], 'generators': [1959914885, 4834230804, 5792262062, 4834220124], 'label': '21600.y.360.u1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '360.u1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947346
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '60.l1.b1', '120.h1.b1', '180.b1.b1'], 'contains': ['720.e1.b1', '720.g1.a1', '720.p1.b1', '1080.k1.b1', '1800.z1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2074, -1, 4557, -1, 2848, -1, 3825, -1], 'generators': [5160, 10320, 1959937465, 1960185294], 'label': '21600.y.360.u1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '360.u1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.u1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947347
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.b1', '180.h1.b1', '180.k1.b1'], 'contains': ['720.i1.a1', '720.n1.b1', '720.q1.b1', '1080.l1.a1', '1800.bb1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4541, -1, 1747, -1, 2931, -1, 3348, -1], 'generators': [43545600, 79839600, 5396700062, 4837847340], 'label': '21600.y.360.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.v1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947348
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.b1', '180.h1.b1', '180.k1.b1'], 'contains': ['720.i1.a1', '720.n1.b1', '720.q1.b1', '1080.l1.a2', '1800.bb1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4541, -1, 1792, -1, 2931, -1, 3391, -1], 'generators': [43545600, 5393071262, 79839600, 4837847340], 'label': '21600.y.360.v1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.v1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.v1.a2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947349
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '180.h1.a1', '180.k1.a1'], 'contains': ['720.i1.b1', '720.n1.a1', '720.q1.a1', '1080.l1.b1', '1800.bb1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4541, -1, 1876, -1, 2931, -1, 1318, -1], 'generators': [43545600, 4917723685, 39918480, 5832140220], 'label': '21600.y.360.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.v1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.v1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947350
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '180.h1.a1', '180.k1.a1'], 'contains': ['720.i1.b1', '720.n1.a1', '720.q1.a1', '1080.l1.b2', '1800.bb1.b2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4541, -1, 1921, -1, 2931, -1, 1361, -1], 'generators': [43545600, 4914094885, 39918480, 5832140220], 'label': '21600.y.360.v1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.v1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.v1.b2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947351
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.k1.a1', '180.b1.b1'], 'contains': ['720.j1.a1', '720.l1.b1', '720.p1.b1', '1080.m1.a1', '1800.bc1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8345, -1, 831, -1, 1167, -1, 4002, -1], 'generators': [10320, 3633960, 1963814094, 1959937465], 'label': '21600.y.360.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '360.w1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947352
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.k1.b1', '180.b1.a1'], 'contains': ['720.j1.b1', '720.l1.a1', '720.p1.a1', '1080.m1.b1', '1800.bc1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8345, -1, 4024, -1, 1167, -1, 2003, -1], 'generators': [1963543685, 4834230804, 4837848924, 5792262062], 'label': '21600.y.360.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.w1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.w1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947353
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.k1.a1', '180.g1.b1', '180.h1.b1'], 'contains': ['720.i1.a1', '720.m1.b1', '720.n1.b1', '1080.m1.a1', '1800.bd1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7857, -1, 969, -1, 1348, -1, 3139, -1], 'generators': [43545600, 4877781660, 79839600, 4837847340], 'label': '21600.y.360.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '360.x1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947354
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.b1.b1', '12.c1.a1'], 'contains': ['72.e1.b1', '120.a1.b1', '120.f1.b1', '144.b1.b1', '240.b1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6222, -1, 5719, -1, 2992, -1, 1312, -1], 'generators': [43545600, 79843920, 80103271, 5312931992], 'label': '21600.y.24.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '240.190'}
  • id: 63947355
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '120.k1.b1', '180.g1.a1', '180.h1.a1'], 'contains': ['720.i1.b1', '720.m1.a1', '720.n1.a1', '1080.m1.b1', '1800.bd1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7857, -1, 1521, -1, 1348, -1, 1109, -1], 'generators': [43545600, 39918480, 4917721261, 5832140220], 'label': '21600.y.360.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '360.x1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.x1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947356
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '120.l1.a1', '180.d1.a1'], 'contains': ['1800.bg1.a1', '2160.h1.a1', '3600.n1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4964, -1, 9799, -1, 9983, -1, 2603, -1], 'generators': [252991, 5312934176], 'label': '21600.y.360.y1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.a1', 'old_label': '360.y1.a1', 'projective_image': '21600.y', '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': '60.5'}
  • id: 63947357
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '360.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '120.l1.b1', '180.d1.b1'], 'contains': ['1800.bg1.a2', '2160.h1.b1', '3600.n1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [4964, -1, 9603, -1, 9983, -1, 2650, -1], 'generators': [299674, 1960245537], 'label': '21600.y.360.y1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.b1', 'old_label': '360.y1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.y1.b1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63947358
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.a1.a1', '100.a1.b1', '200.a1.a1', '200.a1.b1', '200.b1.a1'], 'contains': ['800.a1.a1', '1200.a1.a1', '1200.b1.a1', '1200.b1.b1', '1200.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3443, -1, 6102, -1, 8167, -1, 4925, -1], 'generators': [39916800, 83462640, 43545600, 5875396137], 'label': '21600.y.400.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '400.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947359
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '400.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '100.d1.a1', '200.a1.a1', '200.c1.a1', '200.e1.a1'], 'contains': ['800.a1.a1', '1200.d1.a1', '1200.e1.a1', '1200.f1.a1', '1200.g1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3105, -1, 8258, -1, 5533, -1, 4875, -1], 'generators': [298230, 43545600, 288150, 79838664], 'label': '21600.y.400.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '400.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947360
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '400.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '100.d1.b1', '200.a1.b1', '200.c1.b1', '200.e1.a1'], 'contains': ['800.a1.a1', '1200.d1.b1', '1200.e1.b1', '1200.f1.b1', '1200.g1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3105, -1, 8969, -1, 5533, -1, 4732, -1], 'generators': [79833840, 43545600, 5792221743, 5392806153], 'label': '21600.y.400.b1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '400.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 63947361
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.c1.a1', '200.a1.b1', '200.c1.a1', '200.f1.a1'], 'contains': ['800.a1.a1', '1200.h1.a1', '1200.i1.a1', '1200.j1.a1', '1200.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [4938, -1, 6893, -1, 4321, -1, 5048, -1], 'generators': [79833840, 43545600, 5832138543, 5392806153], 'label': '21600.y.400.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '400.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947362
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.c1.b1', '200.a1.a1', '200.c1.b1', '200.f1.a1'], 'contains': ['800.a1.a1', '1200.h1.b1', '1200.i1.b1', '1200.j1.b1', '1200.k1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [4938, -1, 7014, -1, 4321, -1, 5100, -1], 'generators': [298230, 43545600, 83467464, 288150], 'label': '21600.y.400.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '400.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947363
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '400.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['200.b1.a1', '200.e1.a1', '200.f1.a1'], 'contains': ['800.a1.a1', '1200.l1.a1', '1200.l1.b1', '1200.m1.a1', '1200.n1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6318, -1, 8780, -1, 7974, -1, 5240, -1], 'generators': [79849584, 43545600, 15988, 1959931561], 'label': '21600.y.400.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '400.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 63947364
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '400.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['200.b1.a1', '200.c1.a1', '200.c1.b1'], 'contains': ['800.a1.a1', '1200.o1.a1', '1200.o1.b1', '1200.p1.a1', '1200.q1.a1', '1200.q1.b1', '1200.r1.a1', '1200.s1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6121, -1, 8500, -1, 7788, -1, 5144, -1], 'generators': [79849584, 43545600, 15988, 1999848361], 'label': '21600.y.400.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '400.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 63947365
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.a1.b1'], 'contains': ['50.b1.a1', '75.a1.a1', '75.b1.a1', '75.b1.b1', '75.c1.a1', '75.c1.a2', '100.a1.a1', '100.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [1753, -1, 7567, -1, 7016, -1, 5801, -1], 'generators': [39916800, 5356806064, 43545600, 5875396137, 5832179105, 2424, 1680, 83463240], 'label': '21600.y.25.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '25.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25.a1.a1', 'subgroup_fusion': None, 'weyl_group': '864.4680'}
  • id: 63947366
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '216.a1.a1', '216.a1.b1', '216.b1.a1'], 'contains': ['864.a1.a1', '2160.a1.a1', '2160.a1.b1', '2160.b1.a1', '2160.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9505, -1, 19, -1, 471, -1, 645, -1], 'generators': [39916800, 5832178862, 12360], 'label': '21600.y.432.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947367
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '144.b1.a1', '216.a1.a1', '216.c1.a1', '216.d1.a1'], 'contains': ['864.a1.a1', '2160.c1.a1', '2160.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9131, -1, 2824, -1, 562, -1, 263, -1], 'generators': [5792283806, 5792262062, 12360], 'label': '21600.y.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '432.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947368
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '144.b1.b1', '216.a1.b1', '216.c1.b1', '216.d1.a1'], 'contains': ['864.a1.a1', '2160.c1.b1', '2160.d1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9131, -1, 4811, -1, 562, -1, 133, -1], 'generators': [1959914885, 5792262062, 12360], 'label': '21600.y.432.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '432.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947369
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '216.a1.b1', '216.c1.a1', '216.e1.a1'], 'contains': ['864.a1.a1', '2160.e1.a1', '2160.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9288, -1, 529, -1, 270, -1, 447, -1], 'generators': [2043377285, 5792262062, 12360], 'label': '21600.y.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '432.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947370
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '216.a1.a1', '216.c1.b1', '216.e1.a1'], 'contains': ['864.a1.a1', '2160.e1.b1', '2160.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9288, -1, 294, -1, 270, -1, 403, -1], 'generators': [5832200606, 5792262062, 12360], 'label': '21600.y.432.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '432.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947371
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '216.b1.a1', '216.d1.a1', '216.e1.a1'], 'contains': ['864.a1.a1', '2160.g1.a1', '2160.g1.b1', '2160.h1.a1', '2160.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9572, -1, 4390, -1, 786, -1, 686, -1], 'generators': [4834240284, 5792262062, 12360], 'label': '21600.y.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '432.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947372
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '216.b1.a1', '216.c1.a1', '216.c1.b1'], 'contains': ['864.a1.a1', '2160.i1.a1', '2160.i1.b1', '2160.j1.a1', '2160.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9750, -1, 1186, -1, 731, -1, 605, -1], 'generators': [5792262062, 4837869084, 12360], 'label': '21600.y.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '432.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 63947373
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.b1', '90.b1.a1', '150.a1.a1', '150.b1.a1', '225.a1.b1'], 'contains': ['900.c1.b1', '900.q1.b1', '900.w1.a1', '1350.b1.a1', '1800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3906, -1, 6495, -1, 5844, -1, 8085, -1], 'generators': [5313260464, 5792263745, 1680, 5875397673, 83462400], 'label': '21600.y.450.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.b1', 'old_label': '450.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947374
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.b1.b1', '150.a1.b1', '150.b1.b1', '225.a1.a1'], 'contains': ['900.c1.a1', '900.q1.a1', '900.w1.b1', '1350.b1.b1', '1800.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3906, -1, 4273, -1, 5844, -1, 8968, -1], 'generators': [5313260464, 2424, 1680, 83463240, 83462400], 'label': '21600.y.450.a1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '450.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947375
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.b1', '150.a1.a1', '150.c1.a1'], 'contains': ['900.a1.b1', '900.b1.b1', '900.e1.b1', '900.l1.b1', '900.s1.b1', '900.u1.b1', '900.y1.a1', '1350.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2945, -1, 7720, -1, 6698, -1, 9091, -1], 'generators': [3628800, 4834218540, 4834228620, 1959914882, 4837852404], 'label': '21600.y.450.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '450.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947376
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '10.a1.a1'], 'contains': ['60.b1.b1', '60.j1.b1', '60.l1.a1', '90.b1.a1', '150.a1.a1', '180.b1.a1', '300.b1.a1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 30, 'diagramx': [5842, -1, 5947, -1, 5095, -1, 2679, -1], 'generators': [83479080, 2043398282, 83478384, 83766537, 83462400], 'label': '21600.y.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '21600.y', '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': '360.121'}
  • id: 63947377
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '150.a1.b1', '150.c1.b1'], 'contains': ['900.a1.a1', '900.b1.a1', '900.e1.a1', '900.l1.a1', '900.s1.a1', '900.u1.a1', '900.y1.b1', '1350.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2945, -1, 2748, -1, 6698, -1, 8496, -1], 'generators': [39916800, 5352890793, 2424, 1680, 5792221743], 'label': '21600.y.450.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.b1', 'old_label': '450.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.b1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947378
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.c1.a1'], 'contains': ['900.g1.a1', '900.g1.b1', '900.h1.a1', '900.j1.a1', '900.j1.a2', '900.k1.a1', '900.k1.a2', '900.k1.b1', '900.k1.b2', '900.o1.a1', '900.p1.a1', '900.z1.a1', '900.z1.a2', '1350.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [845, -1, 5464, -1, 8839, -1, 7546, -1], 'generators': [5356808488, 39916800, 43545600, 1680, 5872097345], 'label': '21600.y.450.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '450.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947379
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.b1', '150.b1.a1', '150.c1.a1', '225.c1.a1'], 'contains': ['900.g1.b1', '900.h1.a1', '900.i1.b1', '900.m1.b1', '900.n1.a1', '900.r1.b1', '900.v1.a1', '1350.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3164, -1, 7231, -1, 8196, -1, 7225, -1], 'generators': [39916800, 5356806064, 43545600, 1680, 5872097345], 'label': '21600.y.450.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '450.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947380
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.c1.a1', '150.b1.b1', '150.c1.b1', '225.c1.a1'], 'contains': ['900.g1.a1', '900.h1.a1', '900.i1.a1', '900.m1.a1', '900.n1.b1', '900.r1.a1', '900.v1.b1', '1350.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3164, -1, 3033, -1, 8196, -1, 7028, -1], 'generators': [39916800, 5356806064, 43545600, 2424, 1680], 'label': '21600.y.450.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '450.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.d1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947381
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.c1.a1'], 'contains': ['900.k1.a1', '900.k1.a2', '900.k1.b1', '900.k1.b2', '900.m1.a1', '900.m1.b1', '900.n1.a1', '900.n1.b1', '900.p1.a1', '900.z1.a1', '900.z1.a2', '1350.c1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [685, -1, 5337, -1, 8744, -1, 7448, -1], 'generators': [5356806064, 43545600, 2424, 39918480, 5872097345], 'label': '21600.y.450.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '450.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947382
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.d1.a1', '150.d1.a1', '225.a1.b1'], 'contains': ['900.q1.b1', '900.w1.a1', '1350.d1.a1', '1800.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [1721, -1, 6546, -1, 6043, -1, 8134, -1], 'generators': [5313260464, 5792263745, 39919224, 1680, 5831851137], 'label': '21600.y.450.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.b1', 'old_label': '450.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947383
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.d1.b1', '150.d1.b1', '225.a1.a1'], 'contains': ['900.q1.a1', '900.w1.b1', '1350.d1.b1', '1800.g1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [1721, -1, 7859, -1, 6043, -1, 9041, -1], 'generators': [840, 5313260464, 5832179105, 2424, 1680], 'label': '21600.y.450.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '450.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947384
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.d1.a1', '225.c1.a1'], 'contains': ['900.k1.b1', '900.k1.b2', '900.n1.b1', '900.o1.a1', '900.r1.b1', '900.v1.a1', '1350.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1005, -1, 6587, -1, 8619, -1, 7596, -1], 'generators': [5356806064, 5875726145, 43545600, 2424, 39918480], 'label': '21600.y.450.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '450.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.g1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947385
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.d1.b1', '225.c1.a1'], 'contains': ['900.k1.a1', '900.k1.a2', '900.n1.a1', '900.o1.a1', '900.r1.a1', '900.v1.b1', '1350.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1005, -1, 6240, -1, 8619, -1, 7497, -1], 'generators': [43545600, 2424, 1680, 5316889264, 5872097345], 'label': '21600.y.450.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '450.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.g1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947386
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.e1.a1', '150.e1.b1', '150.f1.a1', '150.f1.a2', '225.c1.a1'], 'contains': ['900.p1.a1', '900.v1.a1', '900.v1.b1', '1350.e1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [545, -1, 7641, -1, 9097, -1, 7645, -1], 'generators': [5356806064, 43545600, 2424, 1680, 5872097345], 'label': '21600.y.450.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '450.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.h1.a1', 'subgroup_fusion': None, 'weyl_group': '18.5'}
  • id: 63947387
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '10.a1.b1'], 'contains': ['60.b1.a1', '60.j1.a1', '60.l1.b1', '90.b1.b1', '150.a1.b1', '180.b1.b1', '300.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5842, -1, 5492, -1, 5095, -1, 4403, -1], 'generators': [83484144, 247832, 1584, 5792221743, 83462400], 'label': '21600.y.30.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '30.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947388
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.b1', '150.e1.a1', '150.g1.a1', '150.h1.a1', '225.a1.a1'], 'contains': ['900.w1.b1', '1350.e1.a1', '1800.t1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [405, -1, 9409, -1, 7492, -1, 9140, -1], 'generators': [840, 5313260464, 2424, 5792262305, 1680], 'label': '21600.y.450.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '450.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 63947389
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '150.e1.b1', '150.g1.b1', '150.h1.a1', '225.a1.b1'], 'contains': ['900.w1.a1', '1350.e1.a1', '1800.t1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [405, -1, 6849, -1, 7492, -1, 8226, -1], 'generators': [5791934337, 5313260464, 5792263745, 2424, 1680], 'label': '21600.y.450.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '450.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.i1.b1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 63947390
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.e1.b1', '150.g1.a1', '150.i1.a1', '150.i1.a2'], 'contains': ['900.x1.a1', '1350.e1.a1', '1800.v1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [36, -1, 9222, -1, 8937, -1, 5775, -1], 'generators': [5835479937, 5313260464, 5792263745, 2424, 1680], 'label': '21600.y.450.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '450.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 63947391
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.e1.a1', '150.g1.b1', '150.i1.a1', '150.i1.a2'], 'contains': ['900.x1.b1', '1350.e1.a1', '1800.v1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [36, -1, 9514, -1, 8937, -1, 6534, -1], 'generators': [43546440, 5313260464, 2424, 1680, 5835807905], 'label': '21600.y.450.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '450.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.j1.b1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 63947392
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.f1.a1', '150.h1.a1', '150.i1.a2', '225.b1.a1'], 'contains': ['1350.e1.a1', '1800.x1.a1', '1800.x1.b1', '1800.bg1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [255, -1, 9549, -1, 9554, -1, 9584, -1], 'generators': [5313260464, 5792263745, 2424, 1680, 5791935177], 'label': '21600.y.450.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '450.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.k1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947393
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.f1.a2', '150.h1.a1', '150.i1.a1', '225.b1.a2'], 'contains': ['1350.e1.a1', '1800.x1.a1', '1800.x1.b1', '1800.bg1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [255, -1, 9599, -1, 9554, -1, 9641, -1], 'generators': [5313260464, 5792263745, 2424, 5791933737, 1680], 'label': '21600.y.450.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '450.k1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.k1.a2', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947394
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.f1.a1', '150.g1.a1', '150.g1.b1', '150.i1.a1'], 'contains': ['1350.e1.a1', '1800.y1.a1', '1800.y1.b1', '1800.bh1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [106, -1, 9667, -1, 9623, -1, 9359, -1], 'generators': [5835480777, 5313260464, 5792263745, 2424, 1680], 'label': '21600.y.450.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '450.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947395
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '450.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.f1.a2', '150.g1.a1', '150.g1.b1', '150.i1.a2'], 'contains': ['1350.e1.a1', '1800.y1.a1', '1800.y1.b1', '1800.bh1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [106, -1, 9748, -1, 9623, -1, 9288, -1], 'generators': [5871767337, 5313260464, 5792263745, 2424, 1680], 'label': '21600.y.450.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '450.l1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.l1.a2', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947396
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.a1', '240.a1.a1', '240.b1.a1', '240.c1.b1', '240.d1.b1', '240.e1.a1', '240.f1.a1', '240.g1.a1'], 'contains': ['1440.a1.a1', '1440.c1.a1', '1440.d1.b1', '2400.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8125, -1, 4226, -1, 2146, -1, 890, -1], 'generators': [5872055580, 79833840, 43545600], 'label': '21600.y.480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '480.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63947397
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.f1.b1', '240.a1.b1', '240.b1.b1', '240.c1.a1', '240.d1.a1', '240.e1.b1', '240.f1.b1', '240.g1.b1'], 'contains': ['1440.a1.b1', '1440.c1.b1', '1440.d1.a1', '2400.a1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8125, -1, 349, -1, 2146, -1, 2926, -1], 'generators': [43545600, 2003708310, 79839600], 'label': '21600.y.480.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '480.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63947398
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '6.b1.b1'], 'contains': ['60.c1.a1', '60.f1.a1', '60.g1.a1', '90.a1.a1', '90.c1.a1', '120.c1.b1', '150.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5062, -1, 4136, -1, 4084, -1, 2046, -1], 'generators': [39916800, 43545600, 4914092461, 2424, 1680, 5875684380, 83463240], 'label': '21600.y.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '30.b1.a1', 'projective_image': '21600.y', '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': '720.797'}
  • id: 63947399
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '270.a1.a1'], 'contains': ['1080.a1.a1', '1080.c1.a1', '1080.g1.a1', '1080.h1.a1', '1080.l1.b1', '1080.l1.b2', '2700.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4329, -1, 3096, -1, 3298, -1, 2299, -1], 'generators': [39916800, 1680, 4834261285, 5792223420], 'label': '21600.y.540.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '540.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947400
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.b1', '270.a1.b1'], 'contains': ['1080.a1.b1', '1080.c1.b1', '1080.g1.b1', '1080.h1.b1', '1080.l1.a1', '1080.l1.a2', '2700.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4329, -1, 3401, -1, 3298, -1, 4329, -1], 'generators': [4834218540, 83468400, 5396700062, 83462400], 'label': '21600.y.540.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '540.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947401
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.f1.a1', '270.a1.a1'], 'contains': ['1080.a1.a1', '1080.e1.a1', '1080.i1.a1', '2700.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5288, -1, 2327, -1, 3823, -1, 2403, -1], 'generators': [39916800, 2424, 1680, 5792223420], 'label': '21600.y.540.b1.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': '540.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947402
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.b1', '180.f1.b1', '270.a1.b1'], 'contains': ['1080.a1.b1', '1080.e1.b1', '1080.i1.b1', '2700.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5288, -1, 7343, -1, 3823, -1, 4445, -1], 'generators': [4834218540, 2043383282, 1959914882, 83462400], 'label': '21600.y.540.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.b1', 'old_label': '540.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947403
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.a1', '108.a1.a1', '180.b1.a1', '180.g1.a1', '270.a1.a1'], 'contains': ['1080.a1.a1', '1080.b1.b1', '1080.c1.a1', '1080.f1.a1', '1080.j1.b1', '1080.k1.a1', '1080.m1.b1', '2700.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7637, -1, 2484, -1, 1757, -1, 2137, -1], 'generators': [39916800, 4834258861, 1680, 5792223420], 'label': '21600.y.540.c1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '540.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947404
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.b1', '108.a1.a1', '180.b1.b1', '180.g1.b1', '270.a1.b1'], 'contains': ['1080.a1.b1', '1080.b1.a1', '1080.c1.b1', '1080.f1.b1', '1080.j1.a1', '1080.k1.b1', '1080.m1.a1', '2700.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7637, -1, 1567, -1, 1757, -1, 4167, -1], 'generators': [4834218540, 83468400, 4834236060, 83462400], 'label': '21600.y.540.c1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '540.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947405
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.h1.a1', '270.a1.a1'], 'contains': ['1080.e1.a1', '1080.f1.a1', '1080.g1.a1', '1080.l1.b1', '1080.l1.b2', '1080.m1.b1', '2700.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4431, -1, 2107, -1, 3104, -1, 2249, -1], 'generators': [83464080, 2424, 4917721261, 5875685820], 'label': '21600.y.540.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '540.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947406
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.h1.b1', '270.a1.b1'], 'contains': ['1080.e1.b1', '1080.f1.b1', '1080.g1.b1', '1080.l1.a1', '1080.l1.a2', '1080.m1.a1', '2700.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4431, -1, 1832, -1, 3104, -1, 4279, -1], 'generators': [4834218540, 5313237662, 2043377282, 2043383282], 'label': '21600.y.540.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '540.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947407
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.j1.a1', '270.a1.a1'], 'contains': ['1080.f1.a1', '1080.h1.a1', '1080.i1.a1', '2700.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5535, -1, 4770, -1, 3720, -1, 2349, -1], 'generators': [2424, 1680, 4917721261, 5792223420], 'label': '21600.y.540.e1.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': '540.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.e1.a1', 'subgroup_fusion': None, 'weyl_group': '30.2'}
  • id: 63947408
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.b1', '180.j1.b1', '270.a1.b1'], 'contains': ['1080.f1.b1', '1080.h1.b1', '1080.i1.b1', '2700.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5535, -1, 7152, -1, 3720, -1, 4391, -1], 'generators': [4834218540, 1959914882, 5396700062, 1959920882], 'label': '21600.y.540.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.b1', 'old_label': '540.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.e1.b1', 'subgroup_fusion': None, 'weyl_group': '30.2'}
  • id: 63947409
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1', '6.b1.a1'], 'contains': ['60.c1.b1', '60.f1.b1', '60.g1.b1', '90.a1.b1', '90.c1.b1', '120.c1.a1', '150.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5062, -1, 7227, -1, 4084, -1, 3751, -1], 'generators': [4877764140, 39916800, 43545600, 1963791510, 2043383282, 1959914882, 5396700062], 'label': '21600.y.30.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '30.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '720.797'}
  • id: 63947410
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.d1.a1', '180.k1.a1', '270.a1.a1'], 'contains': ['1080.e1.a1', '1080.h1.a1', '1080.j1.b1', '1080.k1.a1', '1080.l1.b1', '1080.l1.b2', '2700.g1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [3853, -1, 2790, -1, 3540, -1, 2199, -1], 'generators': [4834258861, 2424, 39918480, 5832140220], 'label': '21600.y.540.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '540.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.f1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947411
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.d1.b1', '180.k1.b1', '270.a1.b1'], 'contains': ['1080.e1.b1', '1080.h1.b1', '1080.j1.a1', '1080.k1.b1', '1080.l1.a1', '1080.l1.a2', '2700.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [3853, -1, 4679, -1, 3540, -1, 4229, -1], 'generators': [4834218540, 2043377282, 2043383282, 5396700062], 'label': '21600.y.540.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '540.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.f1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947412
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '180.l1.a1', '180.m1.a1', '180.n1.a1', '270.a1.a1'], 'contains': ['1080.g1.a1', '1080.i1.a1', '1080.k1.a1', '2700.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1444, -1, 5391, -1, 4704, -1, 2457, -1], 'generators': [4834258861, 2424, 1680, 5792223420], 'label': '21600.y.540.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '540.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.g1.a1', 'subgroup_fusion': None, 'weyl_group': '30.2'}
  • id: 63947413
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '540.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.b1', '180.l1.b1', '180.m1.b1', '180.n1.b1', '270.a1.b1'], 'contains': ['1080.g1.b1', '1080.i1.b1', '1080.k1.b1', '2700.k1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1444, -1, 6671, -1, 4704, -1, 4499, -1], 'generators': [4834218540, 5313237662, 1959914882, 1959920882], 'label': '21600.y.540.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '540.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.g1.b1', 'subgroup_fusion': None, 'weyl_group': '30.2'}
  • id: 63947414
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '150.a1.a1', '200.a1.a1', '300.b1.a1'], 'contains': ['1200.a1.a1', '1200.g1.a1', '1200.j1.b1', '1800.a1.a1', '1800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [3875, -1, 5046, -1, 4935, -1, 8412, -1], 'generators': [83750550, 83467464, 83760630, 83462400], 'label': '21600.y.600.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '600.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947415
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.b1', '150.a1.b1', '200.a1.b1', '300.b1.a1'], 'contains': ['1200.a1.a1', '1200.g1.b1', '1200.j1.a1', '1800.a1.b1', '1800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [3875, -1, 5945, -1, 4935, -1, 8268, -1], 'generators': [83462640, 5312972553, 5792221743, 83462400], 'label': '21600.y.600.a1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '600.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947416
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['200.b1.a1', '300.b1.a1'], 'contains': ['1200.a1.a1', '1200.n1.a1', '1200.r1.a1', '1800.c1.a1', '1800.c1.b1', '1800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [6734, -1, 6778, -1, 7873, -1, 8675, -1], 'generators': [15988, 83478384, 1959931561, 83462400], 'label': '21600.y.600.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '600.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947417
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '150.b1.a1', '200.a1.a1', '300.c1.a1', '300.d1.a1', '300.g1.a1'], 'contains': ['1200.b1.b1', '1200.d1.a1', '1200.h1.b1', '1800.a1.a1', '1800.e1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3458, -1, 1180, -1, 5257, -1, 5287, -1], 'generators': [39916800, 43545600, 1680, 5875397673], 'label': '21600.y.600.c1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947418
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.b1', '150.b1.b1', '200.a1.b1', '300.c1.b1', '300.d1.b1', '300.g1.b1'], 'contains': ['1200.b1.a1', '1200.d1.b1', '1200.h1.a1', '1800.a1.b1', '1800.e1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3458, -1, 4599, -1, 5257, -1, 6127, -1], 'generators': [39916800, 5356806064, 43545600, 83463240], 'label': '21600.y.600.c1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947419
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '120.b1.a1', '200.a1.a1', '300.g1.b1'], 'contains': ['1200.b1.a1', '1200.e1.a1', '1200.k1.b1', '1800.b1.a1', '1800.e1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6641, -1, 4422, -1, 4396, -1, 5829, -1], 'generators': [39916800, 43545600, 83467464, 83472480], 'label': '21600.y.600.d1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '600.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947420
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.a1.a1', '15.b1.a1'], 'contains': ['60.a1.b1', '60.h1.b1', '60.k1.a1', '90.b1.a1', '150.b1.a1', '180.g1.a1', '300.g1.a1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [5733, -1, 4348, -1, 4695, -1, 2401, -1], 'generators': [39916800, 43545600, 5396684222, 5835521191, 1680], 'label': '21600.y.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.c1.a1', 'projective_image': '21600.y', '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': '360.121'}
  • id: 63947421
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.b1', '120.b1.b1', '200.a1.b1', '300.g1.a1'], 'contains': ['1200.b1.b1', '1200.e1.b1', '1200.k1.a1', '1800.b1.b1', '1800.e1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6641, -1, 1386, -1, 4396, -1, 4769, -1], 'generators': [39916800, 43545600, 5352889113, 5792221743], 'label': '21600.y.600.d1.b1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '600.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.d1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947422
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '200.b1.a1', '300.c1.b1', '300.g1.b1'], 'contains': ['1200.b1.a1', '1200.l1.a1', '1200.o1.a1', '1800.c1.a1', '1800.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [7026, -1, 4561, -1, 5883, -1, 5942, -1], 'generators': [39916800, 43545600, 83472480, 4837852404], 'label': '21600.y.600.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947423
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '200.b1.a1', '300.c1.a1', '300.g1.a1'], 'contains': ['1200.b1.b1', '1200.l1.b1', '1200.o1.b1', '1800.c1.b1', '1800.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [7026, -1, 3348, -1, 5883, -1, 5175, -1], 'generators': [39916800, 43545600, 5352889113, 5792223423], 'label': '21600.y.600.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.e1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947424
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '60.e1.b1', '200.b1.a1'], 'contains': ['1200.c1.a1', '1200.m1.a1', '1200.p1.a1', '1800.d1.a1', '1800.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [8818, -1, 8000, -1, 9302, -1, 6598, -1], 'generators': [39916800, 43545600, 15988, 1959931561], 'label': '21600.y.600.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.f1.a1', 'old_label': '600.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947425
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.d1.a1', '300.d1.a1', '300.i1.a1', '300.n1.a1'], 'contains': ['1200.d1.a1', '1200.h1.b1', '1800.g1.a1', '1800.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2377, -1, 2223, -1, 5817, -1, 5530, -1], 'generators': [43545600, 39919224, 1680, 5831851137], 'label': '21600.y.600.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947426
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.d1.b1', '300.d1.b1', '300.i1.b1', '300.n1.b1'], 'contains': ['1200.d1.b1', '1200.h1.a1', '1800.g1.b1', '1800.k1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2377, -1, 7607, -1, 5817, -1, 6397, -1], 'generators': [79833840, 5356806064, 43545600, 5832179105], 'label': '21600.y.600.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947427
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.g1.a1', '200.c1.a1', '300.g1.a1', '300.i1.a1', '300.m1.a1'], 'contains': ['1200.d1.a1', '1200.k1.a1', '1200.o1.b1', '1800.h1.a1', '1800.i1.a1', '1800.j1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6056, -1, 2007, -1, 5630, -1, 5335, -1], 'generators': [5312973993, 43545600, 5832138543, 1680], 'label': '21600.y.600.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947428
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.g1.b1', '200.c1.b1', '300.g1.b1', '300.i1.b1', '300.m1.b1'], 'contains': ['1200.d1.b1', '1200.k1.b1', '1200.o1.a1', '1800.h1.b1', '1800.i1.b1', '1800.j1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6056, -1, 7827, -1, 5630, -1, 6079, -1], 'generators': [4877764140, 43545600, 4877774220, 4837852404], 'label': '21600.y.600.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.h1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947429
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.a1', '300.i1.a1', '300.p1.b1'], 'contains': ['1200.d1.a1', '1200.l1.b1', '1800.l1.a1', '1800.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2250, -1, 4208, -1, 6982, -1, 5487, -1], 'generators': [5312973993, 43545600, 5872057767, 1680], 'label': '21600.y.600.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947430
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.b1', '300.i1.b1', '300.p1.a1'], 'contains': ['1200.d1.b1', '1200.l1.a1', '1800.l1.b1', '1800.m1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2250, -1, 9086, -1, 6982, -1, 6354, -1], 'generators': [4877764140, 43545600, 5393058806, 4877774220], 'label': '21600.y.600.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947431
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.a1.b1', '15.b1.b1'], 'contains': ['60.a1.a1', '60.h1.a1', '60.k1.b1', '90.b1.b1', '150.b1.b1', '180.g1.b1', '300.g1.b1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5733, -1, 4278, -1, 4695, -1, 4138, -1], 'generators': [4877764140, 39916800, 43545600, 4877770740, 4837858164], 'label': '21600.y.30.c1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '30.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947432
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.a1', '300.m1.a1', '300.n1.a1'], 'contains': ['1200.d1.a1', '1200.o1.b1', '1800.n1.a1', '1800.o1.a1', '1800.p1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2832, -1, 2859, -1, 6891, -1, 5439, -1], 'generators': [5312973993, 43545600, 5875686567, 1680], 'label': '21600.y.600.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947433
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.b1', '300.m1.b1', '300.n1.b1'], 'contains': ['1200.d1.b1', '1200.o1.a1', '1800.n1.b1', '1800.o1.b1', '1800.p1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2832, -1, 8805, -1, 6891, -1, 6307, -1], 'generators': [4877764140, 43545600, 4877774220, 5396687606], 'label': '21600.y.600.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.j1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947434
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.a1', '120.e1.a1', '200.c1.a1', '300.g1.b1', '300.n1.b1'], 'contains': ['1200.e1.a1', '1200.h1.a1', '1200.o1.a1', '1800.h1.a1', '1800.r1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [5986, -1, 7072, -1, 5145, -1, 5891, -1], 'generators': [43545600, 4837857420, 4837847340, 4837852404], 'label': '21600.y.600.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947435
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.b1', '120.e1.b1', '200.c1.b1', '300.g1.a1', '300.n1.a1'], 'contains': ['1200.e1.b1', '1200.h1.b1', '1200.o1.b1', '1800.h1.b1', '1800.r1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [5986, -1, 2385, -1, 5145, -1, 4795, -1], 'generators': [5352890793, 43545600, 39918480, 5792221743], 'label': '21600.y.600.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.k1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947436
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.a1', '200.c1.a1'], 'contains': ['1200.f1.a1', '1200.i1.a1', '1200.q1.a1', '1800.j1.a1', '1800.r1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [5399, -1, 7342, -1, 4846, -1, 5564, -1], 'generators': [16680, 2043377281, 43561588, 15984], 'label': '21600.y.600.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.l1.a1', 'old_label': '600.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947437
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.b1', '200.c1.b1'], 'contains': ['1200.f1.b1', '1200.i1.b1', '1200.q1.b1', '1800.j1.b1', '1800.r1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [5399, -1, 8150, -1, 4846, -1, 6216, -1], 'generators': [83479080, 79849584, 1959914881, 79849588], 'label': '21600.y.600.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.l1.b1', 'old_label': '600.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.l1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947438
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.a1', '200.c1.a1', '300.b1.a1'], 'contains': ['1200.g1.a1', '1200.j1.a1', '1200.r1.a1', '1800.i1.a1', '1800.r1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [5868, -1, 7363, -1, 5000, -1, 8378, -1], 'generators': [15988, 16680, 2043377281, 15984], 'label': '21600.y.600.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '600.m1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947439
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.j1.b1', '200.c1.b1', '300.b1.a1'], 'contains': ['1200.g1.b1', '1200.j1.b1', '1200.r1.a1', '1800.i1.b1', '1800.r1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [5868, -1, 5249, -1, 5000, -1, 8234, -1], 'generators': [83479080, 15988, 1959914881, 15984], 'label': '21600.y.600.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '600.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.m1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947440
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.e1.b1', '200.d1.a1', '300.d1.a1', '300.m1.a1', '300.p1.b1'], 'contains': ['1200.d1.a1', '1800.s1.a1', '1800.t1.a1', '1800.v1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1436, -1, 6597, -1, 8072, -1, 5590, -1], 'generators': [5791934337, 43545600, 2424, 1680], 'label': '21600.y.600.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '600.n1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 63947441
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.e1.a1', '200.d1.b1', '300.d1.b1', '300.m1.b1', '300.p1.a1'], 'contains': ['1200.d1.b1', '1800.s1.b1', '1800.t1.b1', '1800.v1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1436, -1, 9357, -1, 8072, -1, 6431, -1], 'generators': [79833840, 5356806064, 43545600, 5792262305], 'label': '21600.y.600.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '600.n1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.n1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 63947442
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.a1', '15.a1.a1', '15.b1.a1', '20.a1.b1', '25.a1.a1', '30.b1.a1', '50.a1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [3334, -1, 6000, -1, 5522, -1, 2785, -1], 'generators': [39916800, 5313220382, 43545600, 5835519751, 2424, 1680, 83463240], 'label': '21600.y.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': '21600.y', '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': '4320.ct'}
  • id: 63947443
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.a1'], 'contains': ['60.h1.b1', '60.k1.a1', '90.d1.a1', '150.d1.a1', '180.k1.a1', '300.n1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [3243, -1, 5109, -1, 5395, -1, 2479, -1], 'generators': [5795604391, 43545600, 5396684222, 2424, 39918480], 'label': '21600.y.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': '21600.y', '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': '360.121'}
  • id: 63947444
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.f1.a1', '200.d1.a1', '300.e1.a1', '300.j1.a1', '300.o1.b1'], 'contains': ['1800.s1.a1', '1800.u1.a1', '1800.w1.a1', '2400.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4726, -1, 8399, -1, 5948, -1, 5795, -1], 'generators': [43545600, 2424, 79834440, 1680], 'label': '21600.y.600.o1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '600.o1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947445
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.b1', '120.f1.b1', '200.d1.b1', '300.e1.b1', '300.j1.b1', '300.o1.a1'], 'contains': ['1800.s1.b1', '1800.u1.b1', '1800.w1.b1', '2400.a1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4726, -1, 8285, -1, 5948, -1, 4558, -1], 'generators': [5356806064, 5872095665, 43545600, 5871767193], 'label': '21600.y.600.o1.b1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '600.o1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.o1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947446
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.f1.a1', '150.f1.a2', '200.d1.a1', '300.f1.a1'], 'contains': ['1800.s1.a1', '1800.x1.a1', '1800.y1.a1', '2400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1101, -1, 9409, -1, 9663, -1, 6797, -1], 'generators': [5871767337, 43545600, 2424, 1680], 'label': '21600.y.600.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '600.p1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947447
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.f1.a1', '150.f1.a2', '200.d1.b1', '300.f1.b1'], 'contains': ['1800.s1.b1', '1800.x1.b1', '1800.y1.b1', '2400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1101, -1, 9981, -1, 9663, -1, 6742, -1], 'generators': [5356806064, 5872095665, 5871767337, 43545600], 'label': '21600.y.600.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.b1', 'old_label': '600.p1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947448
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.g1.b1', '200.d1.a1', '300.q1.b1'], 'contains': ['1800.t1.a1', '1800.w1.a1', '1800.y1.a1', '2400.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [50, -1, 9483, -1, 7689, -1, 5989, -1], 'generators': [2424, 5835479337, 79834440, 1680], 'label': '21600.y.600.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.d1.b1', 'old_label': '600.q1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947449
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.g1.a1', '200.d1.b1', '300.q1.a1'], 'contains': ['1800.t1.b1', '1800.w1.b1', '1800.y1.b1', '2400.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [50, -1, 9250, -1, 7689, -1, 4643, -1], 'generators': [5871767337, 5313260464, 240, 5792262305], 'label': '21600.y.600.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.d1.a1', 'old_label': '600.q1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.q1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947450
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.a1', '150.g1.a1', '200.d1.a1', '300.k1.a1'], 'contains': ['1800.u1.a1', '1800.v1.a1', '1800.y1.a1', '2400.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1588, -1, 8856, -1, 7254, -1, 5624, -1], 'generators': [840, 2424, 5835479337, 1680], 'label': '21600.y.600.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.c1.a1', 'old_label': '600.r1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947451
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.b1', '150.g1.b1', '200.d1.b1', '300.k1.b1'], 'contains': ['1800.u1.b1', '1800.v1.b1', '1800.y1.b1', '2400.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1588, -1, 9926, -1, 7254, -1, 6466, -1], 'generators': [5871767337, 5313260464, 43545840, 5835807905], 'label': '21600.y.600.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.c1.b1', 'old_label': '600.r1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.r1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947452
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.j1.a1', '150.h1.a1', '200.d1.a1', '300.a1.a1', '300.l1.a1', '300.r1.b1'], 'contains': ['1800.t1.a1', '1800.u1.a1', '1800.x1.a1', '2400.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1496, -1, 8637, -1, 7336, -1, 8553, -1], 'generators': [840, 2424, 5791933737, 1680], 'label': '21600.y.600.s1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '600.s1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.s1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947453
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.j1.b1', '150.h1.a1', '200.d1.b1', '300.a1.b1', '300.l1.b1', '300.r1.a1'], 'contains': ['1800.t1.b1', '1800.u1.b1', '1800.x1.b1', '2400.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1496, -1, 9329, -1, 7336, -1, 8000, -1], 'generators': [5313260464, 240, 5792262305, 5791933737], 'label': '21600.y.600.s1.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '600.s1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.s1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947454
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.b1'], 'contains': ['60.h1.a1', '60.k1.b1', '90.d1.b1', '150.d1.b1', '180.k1.b1', '300.n1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3243, -1, 7346, -1, 5395, -1, 4216, -1], 'generators': [4877764140, 5396689142, 43545600, 5396693366, 1999831682], 'label': '21600.y.30.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '30.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947455
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.i1.a1', '150.i1.a2', '200.d1.a1'], 'contains': ['1800.v1.a1', '1800.w1.a1', '1800.x1.a1', '1800.y1.a1', '2400.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [484, -1, 9284, -1, 9531, -1, 5667, -1], 'generators': [5871767337, 2424, 79834440, 1680], 'label': '21600.y.600.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.d1.a1', 'old_label': '600.t1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947456
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.i1.a1', '150.i1.a2', '200.d1.b1'], 'contains': ['1800.v1.b1', '1800.w1.b1', '1800.x1.b1', '1800.y1.b1', '2400.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [484, -1, 9891, -1, 9531, -1, 4600, -1], 'generators': [5313260464, 43545840, 5835479337, 5835807905], 'label': '21600.y.600.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.d1.b1', 'old_label': '600.t1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.t1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947457
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '120.h1.b1', '200.e1.a1', '300.g1.a1', '300.n1.a1', '300.p1.b1'], 'contains': ['1200.d1.a1', '1200.e1.b1', '1200.l1.b1', '1800.q1.a1', '1800.z1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [1836, -1, 4902, -1, 6030, -1, 4829, -1], 'generators': [5312973993, 43545600, 1680, 5792221743], 'label': '21600.y.600.u1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.u1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947458
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.b1', '120.h1.a1', '200.e1.a1', '300.g1.b1', '300.n1.b1', '300.p1.a1'], 'contains': ['1200.d1.b1', '1200.e1.a1', '1200.l1.a1', '1800.q1.a1', '1800.z1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [1836, -1, 8673, -1, 6030, -1, 6031, -1], 'generators': [4877764140, 4877769204, 43545600, 4877774220], 'label': '21600.y.600.u1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.u1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.u1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947459
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a1', '60.l1.b1', '200.e1.a1', '300.b1.a1'], 'contains': ['1200.g1.a1', '1200.g1.b1', '1200.n1.a1', '1800.z1.a1', '1800.z1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3554, -1, 8745, -1, 5705, -1, 8302, -1], 'generators': [15988, 16680, 1959914881, 15984], 'label': '21600.y.600.v1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '600.v1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.v1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947460
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.b1', '300.i1.b1', '300.n1.b1'], 'contains': ['1200.h1.a1', '1200.l1.a1', '1200.o1.a1', '1800.ba1.a1', '1800.bb1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2768, -1, 7451, -1, 6391, -1, 6242, -1], 'generators': [43545600, 4837857420, 5396687606, 4837847340], 'label': '21600.y.600.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.w1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.w1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947461
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.b1', '300.i1.b1', '300.n1.b1'], 'contains': ['1200.h1.a1', '1200.l1.a1', '1200.o1.a1', '1800.ba1.a2', '1800.bb1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2768, -1, 7222, -1, 6391, -1, 6267, -1], 'generators': [43545600, 5393058806, 4837857420, 4837847340], 'label': '21600.y.600.w1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.w1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.w1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947462
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.a1', '300.i1.a1', '300.n1.a1'], 'contains': ['1200.h1.b1', '1200.l1.b1', '1200.o1.b1', '1800.ba1.b1', '1800.bb1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2768, -1, 1873, -1, 6391, -1, 5374, -1], 'generators': [5352890793, 43545600, 39918480, 5875686567], 'label': '21600.y.600.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.w1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.w1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947463
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.a1', '300.i1.a1', '300.n1.a1'], 'contains': ['1200.h1.b1', '1200.l1.b1', '1200.o1.b1', '1800.ba1.b2', '1800.bb1.b2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2768, -1, 1946, -1, 6391, -1, 5400, -1], 'generators': [5352890793, 43545600, 5872057767, 39918480], 'label': '21600.y.600.w1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.w1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.w1.b2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947464
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['200.f1.a1', '300.b1.a1'], 'contains': ['1200.j1.a1', '1200.j1.b1', '1200.n1.a1', '1800.bc1.a1', '1800.bc1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [6553, -1, 6052, -1, 4492, -1, 8624, -1], 'generators': [83479080, 15988, 2043377281, 15984], 'label': '21600.y.600.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '600.x1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.x1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947465
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '15.b1.a1'], 'contains': ['60.k1.a1', '90.e1.a1', '150.e1.b1', '180.l1.a1', '300.p1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1649, -1, 5354, -1, 5862, -1, 2546, -1], 'generators': [43545600, 5393055422, 2424, 5835521191, 1680], 'label': '21600.y.30.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '21600.y', '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': '360.122'}
  • id: 63947466
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.k1.b1', '200.f1.a1', '300.g1.b1', '300.i1.b1'], 'contains': ['1200.h1.a1', '1200.k1.b1', '1200.l1.a1', '1800.bc1.a1', '1800.bd1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6839, -1, 6736, -1, 4541, -1, 5917, -1], 'generators': [4877769204, 43545600, 4837857420, 4837847340], 'label': '21600.y.600.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '600.y1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.y1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947467
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.k1.a1', '200.f1.a1', '300.g1.a1', '300.i1.a1'], 'contains': ['1200.h1.b1', '1200.k1.a1', '1200.l1.b1', '1800.bc1.b1', '1800.bd1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6839, -1, 1365, -1, 4541, -1, 5201, -1], 'generators': [5352890793, 43545600, 5832138543, 39918480], 'label': '21600.y.600.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '600.y1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.y1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947468
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.a1', '150.f1.a2', '300.h1.a1'], 'contains': ['1800.bf1.a1', '1800.bg1.a1', '1800.bh1.a2', '2400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4478, -1, 9846, -1, 9897, -1, 6632, -1], 'generators': [5871767337, 43545600, 5872096409, 5356807744], 'label': '21600.y.600.z1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a1', 'old_label': '600.z1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.z1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947469
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '600.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.b1', '150.f1.a1', '300.h1.a2'], 'contains': ['1800.bf1.a2', '1800.bg1.a2', '1800.bh1.a1', '2400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4478, -1, 9753, -1, 9897, -1, 6687, -1], 'generators': [43545600, 5792264489, 5791935177, 5356807744], 'label': '21600.y.600.z1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a2', 'old_label': '600.z1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.z1.a2', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63947470
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '675.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.a1.a1', '225.a1.b1', '225.b1.a1', '225.b1.a2', '225.c1.a1'], 'contains': ['1350.a1.a1', '1350.b1.a1', '1350.b1.b1', '1350.c1.a1', '1350.d1.a1', '1350.d1.b1', '1350.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [538, -1, 7475, -1, 9021, -1, 9847, -1], 'generators': [39916800, 5313260464, 5792263745, 2424, 1680], 'label': '21600.y.675.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '675.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '675.a1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 63947471
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '240.a1.a1', '360.b1.a1', '360.c1.b1', '360.d1.a1'], 'contains': ['1440.c1.a1', '2160.a1.a1', '3600.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7858, -1, 3699, -1, 1807, -1, 1922, -1], 'generators': [83462640, 5875684380, 83462400], 'label': '21600.y.720.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '720.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947472
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.b1', '240.a1.b1', '360.b1.b1', '360.c1.a1', '360.d1.b1'], 'contains': ['1440.c1.b1', '2160.a1.b1', '3600.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7858, -1, 127, -1, 1807, -1, 3892, -1], 'generators': [2043625110, 83468400, 83462400], 'label': '21600.y.720.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '720.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947473
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.a1.a1', '360.e1.a1', '360.f1.b1', '360.g1.a1'], 'contains': ['1440.a1.a1', '2160.a1.a1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7920, -1, 468, -1, 1604, -1, 1166, -1], 'generators': [39916800, 43545600, 5792221740], 'label': '21600.y.720.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '720.b1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947474
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.a1.b1', '360.e1.b1', '360.f1.a1', '360.g1.b1'], 'contains': ['1440.a1.b1', '2160.a1.b1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7920, -1, 229, -1, 1604, -1, 3193, -1], 'generators': [39916800, 43545600, 83468400], 'label': '21600.y.720.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947475
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '360.h1.a1'], 'contains': ['1440.b1.a1', '2160.b1.a1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9775, -1, 503, -1, 3129, -1, 2462, -1], 'generators': [39916800, 43545600, 4913776353], 'label': '21600.y.720.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '720.c1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947476
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '15.b1.b1'], 'contains': ['60.k1.b1', '90.e1.b1', '150.e1.a1', '180.l1.b1', '300.p1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1649, -1, 8572, -1, 5862, -1, 4325, -1], 'generators': [5393064566, 4877764140, 43545600, 1959914882, 5393060342], 'label': '21600.y.30.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '30.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.b1', 'subgroup_fusion': None, 'weyl_group': '360.122'}
  • id: 63947477
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '360.h1.b1'], 'contains': ['1440.b1.b1', '2160.b1.b1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9775, -1, 345, -1, 3129, -1, 2617, -1], 'generators': [39916800, 43545600, 5832191222], 'label': '21600.y.720.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '720.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947478
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '240.b1.a1', '360.e1.a1', '360.i1.a1', '360.j1.a1', '360.k1.a1', '360.l1.a1', '360.n1.a1', '360.t1.a1'], 'contains': ['1440.a1.a1', '2160.c1.a1', '3600.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5649, -1, 2980, -1, 3197, -1, 1360, -1], 'generators': [43545600, 1680, 5792223420], 'label': '21600.y.720.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '720.d1.a1', 'projective_image': '21600.y', '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': '4.2'}
  • id: 63947479
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.b1', '240.b1.b1', '360.e1.b1', '360.i1.b1', '360.j1.b1', '360.k1.b1', '360.l1.b1', '360.n1.b1', '360.t1.b1'], 'contains': ['1440.a1.b1', '2160.c1.b1', '3600.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5649, -1, 5641, -1, 3197, -1, 3401, -1], 'generators': [4877764140, 43545600, 79839600], 'label': '21600.y.720.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '720.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947480
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '240.b1.a1', '360.b1.a1', '360.m1.a1', '360.u1.a1'], 'contains': ['1440.c1.a1', '2160.c1.a1', '3600.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8936, -1, 3848, -1, 2644, -1, 1717, -1], 'generators': [5792274326, 5792263646, 5792262062], 'label': '21600.y.720.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '720.e1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947481
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '240.b1.b1', '360.b1.b1', '360.m1.b1', '360.u1.b1'], 'contains': ['1440.c1.b1', '2160.c1.b1', '3600.g1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8936, -1, 5531, -1, 2644, -1, 3758, -1], 'generators': [1959936721, 10320, 1960184550], 'label': '21600.y.720.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '720.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947482
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '144.b1.a1', '240.c1.a1', '360.f1.a1', '360.q1.a1', '360.t1.b1'], 'contains': ['1440.a1.b1', '2160.d1.a1', '3600.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5787, -1, 2891, -1, 2399, -1, 3096, -1], 'generators': [43545600, 17520, 79839600], 'label': '21600.y.720.f1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.f1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947483
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.b1', '144.b1.b1', '240.c1.b1', '360.f1.b1', '360.q1.b1', '360.t1.a1'], 'contains': ['1440.a1.a1', '2160.d1.b1', '3600.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5787, -1, 5779, -1, 2399, -1, 1066, -1], 'generators': [43545600, 4914092461, 5792221740], 'label': '21600.y.720.f1.b1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '720.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.f1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947484
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.j1.a1', '180.m1.b1', '240.c1.a1', '360.c1.a1', '360.r1.a1', '360.u1.b1'], 'contains': ['1440.c1.b1', '2160.d1.a1', '3600.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2093, -1, 2633, -1, 2863, -1, 3813, -1], 'generators': [6000, 17520, 1960162710], 'label': '21600.y.720.g1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '720.g1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947485
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.j1.b1', '180.m1.a1', '240.c1.b1', '360.c1.b1', '360.r1.b1', '360.u1.a1'], 'contains': ['1440.c1.a1', '2160.d1.b1', '3600.e1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [2093, -1, 5825, -1, 2863, -1, 1772, -1], 'generators': [4834258861, 240, 5792221980], 'label': '21600.y.720.g1.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '720.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.g1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947486
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.a1', '180.n1.b1', '240.c1.a1', '360.s1.a1'], 'contains': ['1440.d1.a1', '2160.d1.a1', '3600.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [2204, -1, 3670, -1, 2946, -1, 3644, -1], 'generators': [6000, 17520, 2003708310], 'label': '21600.y.720.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1.a1', 'old_label': '720.h1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947487
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['90.e1.a1', '120.i1.b1', '150.g1.b1', '180.n1.a1', '300.q1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [1115, -1, 8637, -1, 6078, -1, 2600, -1], 'generators': [43546440, 5356765982, 5835519751, 2424, 1680], 'label': '21600.y.30.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '30.f1.a1', 'projective_image': '21600.y', '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': '720.768'}
  • id: 63947488
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.b1', '180.n1.a1', '240.c1.b1', '360.s1.b1'], 'contains': ['1440.d1.b1', '2160.d1.b1', '3600.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [2204, -1, 5998, -1, 2946, -1, 1603, -1], 'generators': [5872055580, 79833840, 4834258861], 'label': '21600.y.720.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1.b1', 'old_label': '720.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.h1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947489
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '240.d1.a1', '360.e1.b1', '360.i1.b1', '360.q1.a1', '360.v1.a1', '360.v1.a2', '360.x1.a1'], 'contains': ['1440.a1.b1', '2160.e1.a1', '3600.i1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7577, -1, 844, -1, 1875, -1, 3246, -1], 'generators': [43545600, 79839600, 4837847340], 'label': '21600.y.720.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '720.i1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947490
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '240.d1.b1', '360.e1.a1', '360.i1.a1', '360.q1.b1', '360.v1.b1', '360.v1.b2', '360.x1.b1'], 'contains': ['1440.a1.a1', '2160.e1.b1', '3600.i1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7577, -1, 809, -1, 1875, -1, 1215, -1], 'generators': [43545600, 39918480, 5832140220], 'label': '21600.y.720.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '720.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947491
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '360.b1.b1', '360.r1.a1', '360.w1.a1'], 'contains': ['1440.c1.b1', '2160.e1.a1', '3600.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8705, -1, 666, -1, 1740, -1, 3928, -1], 'generators': [1999853521, 10320, 1960184550], 'label': '21600.y.720.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '720.j1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947492
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.b1', '360.b1.a1', '360.r1.b1', '360.w1.b1'], 'contains': ['1440.c1.a1', '2160.e1.b1', '3600.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8705, -1, 4005, -1, 1740, -1, 1859, -1], 'generators': [5832191126, 5792263646, 5792262062], 'label': '21600.y.720.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '720.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947493
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '360.s1.a1'], 'contains': ['1440.d1.a1', '2160.e1.a1', '3600.k1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7203, -1, 3484, -1, 1957, -1, 3687, -1], 'generators': [1999853521, 10320, 2003730150], 'label': '21600.y.720.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.s1.a1', 'old_label': '720.k1.a1', 'projective_image': '21600.y', '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': '12.4'}
  • id: 63947494
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.b1', '360.s1.b1'], 'contains': ['1440.d1.b1', '2160.e1.b1', '3600.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7203, -1, 5035, -1, 1957, -1, 1646, -1], 'generators': [5832191126, 5872097246, 5792262062], 'label': '21600.y.720.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.s1.b1', 'old_label': '720.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947495
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '240.e1.a1', '360.c1.b1', '360.m1.a1', '360.w1.b1'], 'contains': ['1440.c1.a1', '2160.f1.a1', '3600.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8118, -1, 3906, -1, 1521, -1, 1816, -1], 'generators': [240, 4917721261, 5792221980], 'label': '21600.y.720.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '720.l1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947496
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.b1', '240.e1.b1', '360.c1.a1', '360.m1.b1', '360.w1.a1'], 'contains': ['1440.c1.b1', '2160.f1.b1', '3600.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [8118, -1, 410, -1, 1521, -1, 3856, -1], 'generators': [6000, 1960162710, 39934320], 'label': '21600.y.720.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '720.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.l1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947497
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '240.e1.a1', '360.f1.b1', '360.j1.a1', '360.x1.b1'], 'contains': ['1440.a1.a1', '2160.f1.a1', '3600.i1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8204, -1, 902, -1, 1373, -1, 1123, -1], 'generators': [43545600, 4917721261, 5792221740], 'label': '21600.y.720.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '720.m1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947498
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1'], 'contains': ['90.e1.b1', '120.i1.a1', '150.g1.a1', '180.n1.b1', '300.q1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1115, -1, 8486, -1, 6078, -1, 4271, -1], 'generators': [4834218540, 5356484192, 2003708310, 1959914882, 5313230966], 'label': '21600.y.30.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '30.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.b1', 'subgroup_fusion': None, 'weyl_group': '720.768'}
  • id: 63947499
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '240.e1.b1', '360.f1.a1', '360.j1.b1', '360.x1.a1'], 'contains': ['1440.a1.b1', '2160.f1.b1', '3600.i1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8204, -1, 439, -1, 1373, -1, 3149, -1], 'generators': [43545600, 79839600, 39934320], 'label': '21600.y.720.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '720.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.m1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947500
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.f1.a1', '360.g1.a1', '360.k1.a1', '360.t1.a1', '360.v1.b1', '360.v1.b2', '360.x1.b1'], 'contains': ['1440.a1.a1', '2160.g1.a1', '3600.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8342, -1, 4673, -1, 2780, -1, 1287, -1], 'generators': [43545600, 4914094141, 5792221740], 'label': '21600.y.720.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '720.n1.a1', 'projective_image': '21600.y', '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': '20.4'}
  • id: 63947501
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '240.f1.b1', '360.g1.b1', '360.k1.b1', '360.t1.b1', '360.v1.a1', '360.v1.a2', '360.x1.a1'], 'contains': ['1440.a1.b1', '2160.g1.b1', '3600.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8342, -1, 4226, -1, 2780, -1, 3317, -1], 'generators': [43545600, 5393071262, 79839600], 'label': '21600.y.720.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '720.n1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.n1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947503
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.b1', '144.d1.a1', '360.h1.b1'], 'contains': ['1440.b1.b1', '2160.h1.b1', '3600.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9906, -1, 4559, -1, 3989, -1, 2660, -1], 'generators': [43545600, 4877785884, 5792274422], 'label': '21600.y.720.o1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.b1', 'old_label': '720.o1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.o1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 63947504
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.f1.a1', '360.d1.a1', '360.u1.a1', '360.w1.b1'], 'contains': ['1440.c1.a1', '2160.g1.a1', '3600.m1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8624, -1, 4731, -1, 2711, -1, 1950, -1], 'generators': [4834230804, 5792263646, 5792262062], 'label': '21600.y.720.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '720.p1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947505
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.f1.b1', '360.d1.b1', '360.u1.b1', '360.w1.a1'], 'contains': ['1440.c1.b1', '2160.g1.b1', '3600.m1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8624, -1, 3731, -1, 2711, -1, 3991, -1], 'generators': [10320, 1960184550, 1959937465], 'label': '21600.y.720.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '720.p1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.p1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947506
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.g1.a1', '360.g1.a1', '360.j1.a1', '360.l1.a1', '360.q1.b1', '360.v1.b1', '360.v1.b2'], 'contains': ['1440.a1.a1', '2160.i1.a1', '3600.o1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7994, -1, 1695, -1, 2576, -1, 1251, -1], 'generators': [43545600, 4917722941, 5792221740], 'label': '21600.y.720.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '720.q1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947507
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '240.g1.b1', '360.g1.b1', '360.j1.b1', '360.l1.b1', '360.q1.a1', '360.v1.a1', '360.v1.a2'], 'contains': ['1440.a1.b1', '2160.i1.b1', '3600.o1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7994, -1, 1038, -1, 2576, -1, 3281, -1], 'generators': [43545600, 79839600, 5396700062], 'label': '21600.y.720.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '720.q1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.q1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947508
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '360.h1.a1'], 'contains': ['1440.b1.a1', '2160.j1.a1', '3600.o1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9964, -1, 1502, -1, 3866, -1, 2427, -1], 'generators': [43545600, 4913776353, 4837869084], 'label': '21600.y.720.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.a1', 'old_label': '720.r1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947509
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['90.e1.a1', '120.j1.b1', '150.h1.a1', '180.m1.a1', '300.r1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1470, -1, 6924, -1, 5663, -1, 2733, -1], 'generators': [5791974151, 840, 5313220382, 2424, 1680], 'label': '21600.y.30.g1.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.g1.a1', 'projective_image': '21600.y', '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': '720.768'}
  • id: 63947510
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '360.h1.b1'], 'contains': ['1440.b1.b1', '2160.j1.b1', '3600.o1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9964, -1, 1273, -1, 3866, -1, 2581, -1], 'generators': [43545600, 5792274422, 4837869084], 'label': '21600.y.720.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.b1', 'old_label': '720.r1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.r1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947511
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.a1', '360.d1.a1', '360.m1.a1', '360.r1.b1'], 'contains': ['1440.c1.a1', '2160.i1.a1', '3600.p1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [9125, -1, 3950, -1, 2277, -1, 1894, -1], 'generators': [4837859604, 5792263646, 5792262062], 'label': '21600.y.720.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '720.s1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947512
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.b1', '360.d1.b1', '360.m1.b1', '360.r1.a1'], 'contains': ['1440.c1.b1', '2160.i1.b1', '3600.p1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [9125, -1, 925, -1, 2277, -1, 3963, -1], 'generators': [10320, 1960184550, 1999854265], 'label': '21600.y.720.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.b1', 'old_label': '720.s1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.s1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947513
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.b1', '360.s1.a1'], 'contains': ['1440.d1.a1', '2160.i1.b1', '3600.q1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7320, -1, 3610, -1, 2331, -1, 3723, -1], 'generators': [10320, 2003730150, 1999854265], 'label': '21600.y.720.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.s1.a1', 'old_label': '720.t1.a1', 'projective_image': '21600.y', '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': '60.8'}
  • id: 63947514
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '720.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.a1', '360.s1.b1'], 'contains': ['1440.d1.b1', '2160.i1.a1', '3600.q1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7320, -1, 4957, -1, 2331, -1, 1682, -1], 'generators': [5872097246, 4837859604, 5792262062], 'label': '21600.y.720.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.s1.b1', 'old_label': '720.t1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.t1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 63947515
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['200.d1.a1', '200.d1.b1', '400.a1.a1', '400.b1.a1', '400.b1.b1', '400.c1.a1', '400.c1.b1', '400.d1.a1', '400.e1.a1'], 'contains': ['2400.a1.a1', '2400.a1.b1', '2400.b1.a1', '2400.c1.a1', '2400.c1.b1', '2400.d1.a1', '2400.e1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3802, -1, 8774, -1, 7145, -1, 5144, -1], 'generators': [79833840, 5871767337, 43545600], 'label': '21600.y.800.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '800.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63947516
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '864.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '432.a1.a1', '432.b1.a1', '432.b1.b1', '432.c1.a1', '432.c1.b1', '432.d1.a1', '432.e1.a1'], 'contains': ['4320.a1.a1', '4320.a1.b1', '4320.b1.a1', '4320.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9494, -1, 246, -1, 692, -1, 625, -1], 'generators': [5792262062, 12360], 'label': '21600.y.864.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '864.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947517
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.a1', '450.b1.b1'], 'contains': ['1800.a1.a1', '1800.c1.b1', '1800.m1.a1', '1800.o1.a1', '1800.ba1.b1', '1800.ba1.b2', '2700.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2683, -1, 2815, -1, 6698, -1, 8738, -1], 'generators': [5396436393, 5875686567, 1680, 83462400], 'label': '21600.y.900.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '900.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947518
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.c1.b1', '450.b1.a1'], 'contains': ['1800.a1.b1', '1800.c1.a1', '1800.m1.b1', '1800.o1.b1', '1800.ba1.a1', '1800.ba1.a2', '2700.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2683, -1, 7113, -1, 6698, -1, 9235, -1], 'generators': [4834218540, 4834228620, 5396687606, 83462400], 'label': '21600.y.900.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '900.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947519
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.a1.b1', '300.a1.a1', '300.d1.a1', '450.b1.b1'], 'contains': ['1800.a1.a1', '1800.g1.a1', '1800.t1.a1', '2700.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2041, -1, 2695, -1, 6463, -1, 8934, -1], 'generators': [39916800, 5791934337, 2424, 1680], 'label': '21600.y.900.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.b1', 'old_label': '900.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947520
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.b1', '15.a1.b1'], 'contains': ['90.e1.b1', '120.j1.a1', '150.h1.a1', '180.m1.b1', '300.r1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1470, -1, 8735, -1, 5663, -1, 4458, -1], 'generators': [4834218540, 5312938592, 1960162710, 1959914882, 5313230966], 'label': '21600.y.30.g1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '30.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.g1.b1', 'subgroup_fusion': None, 'weyl_group': '720.768'}
  • id: 63947521
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.a1.a1', '300.a1.b1', '300.d1.b1', '450.b1.a1'], 'contains': ['1800.a1.b1', '1800.g1.b1', '1800.t1.b1', '2700.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2041, -1, 8085, -1, 6463, -1, 9444, -1], 'generators': [39916800, 5313260464, 39917040, 5832179105], 'label': '21600.y.900.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '900.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947522
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.c1.a1', '300.a1.a1', '300.e1.a1', '450.a1.b1'], 'contains': ['1800.u1.a1', '2700.c1.a1', '3600.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5353, -1, 4121, -1, 5362, -1, 8980, -1], 'generators': [2424, 1680, 83463240, 83462400], 'label': '21600.y.900.c1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '900.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947523
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.b1', '180.c1.b1', '300.a1.b1', '300.e1.b1', '450.a1.a1'], 'contains': ['1800.u1.b1', '2700.c1.b1', '3600.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5353, -1, 6182, -1, 5362, -1, 8042, -1], 'generators': [5875395993, 5313260464, 5792262065, 83462400], 'label': '21600.y.900.c1.b1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '900.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947524
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.b1.a1', '225.b1.a2', '300.a1.a1', '300.f1.a1'], 'contains': ['1800.x1.a1', '2700.c1.a1', '3600.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [1309, -1, 6758, -1, 9236, -1, 9800, -1], 'generators': [5875396137, 2424, 1680, 83462400], 'label': '21600.y.900.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.a1.a1', 'old_label': '900.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947525
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.b1.a1', '225.b1.a2', '300.a1.b1', '300.f1.b1'], 'contains': ['1800.x1.b1', '2700.c1.b1', '3600.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [1309, -1, 8228, -1, 9236, -1, 9757, -1], 'generators': [5313260464, 5875396137, 5792262065, 83462400], 'label': '21600.y.900.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.a1.b1', 'old_label': '900.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947526
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.a1', '180.b1.b1', '300.b1.a1', '300.g1.a1', '450.b1.b1'], 'contains': ['1800.a1.a1', '1800.b1.b1', '1800.c1.b1', '1800.i1.a1', '1800.r1.b1', '1800.z1.a1', '1800.bc1.b1', '2700.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [6869, -1, 2348, -1, 5072, -1, 8340, -1], 'generators': [39916800, 5352890793, 1680, 5792221743], 'label': '21600.y.900.e1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '900.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947527
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.b1', '180.b1.a1', '300.b1.a1', '300.g1.b1', '450.b1.a1'], 'contains': ['1800.a1.b1', '1800.b1.a1', '1800.c1.a1', '1800.i1.b1', '1800.r1.a1', '1800.z1.b1', '1800.bc1.a1', '2700.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [6869, -1, 4685, -1, 5072, -1, 9069, -1], 'generators': [3628800, 4834218540, 4834228620, 4837852404], 'label': '21600.y.900.e1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '900.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947528
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.a1', '225.b1.a2', '300.h1.a1'], 'contains': ['1800.bg1.a1', '2700.d1.a1', '3600.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [5263, -1, 7909, -1, 9769, -1, 9666, -1], 'generators': [5875396137, 5792262809, 5396724544, 83462400], 'label': '21600.y.900.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.f1.a1', 'old_label': '900.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947529
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.b1', '225.b1.a1', '300.h1.a2'], 'contains': ['1800.bg1.a2', '2700.d1.a2', '3600.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [5263, -1, 8123, -1, 9769, -1, 9611, -1], 'generators': [3628800, 5316890944, 5791935177, 5795893289], 'label': '21600.y.900.f1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.f1.a2', 'old_label': '900.f1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.f1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947530
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '300.c1.a1', '450.c1.a1', '450.d1.b1'], 'contains': ['1800.e1.a1', '1800.f1.a1', '1800.l1.a1', '1800.n1.a1', '1800.bb1.b1', '1800.bb1.b2', '2700.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3142, -1, 3387, -1, 8406, -1, 7052, -1], 'generators': [5356808488, 39916800, 43545600, 1680], 'label': '21600.y.900.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947531
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.b1'], 'contains': ['72.e1.a1', '180.a1.a1', '180.c1.a1', '216.a1.a1', '360.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6999, -1, 2568, -1, 2742, -1, 1697, -1], 'generators': [39916800, 5792273582, 5832178862, 5792264246], 'label': '21600.y.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947532
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.b1', '300.c1.b1', '450.c1.a1', '450.d1.a1'], 'contains': ['1800.e1.b1', '1800.f1.a1', '1800.l1.b1', '1800.n1.b1', '1800.bb1.a1', '1800.bb1.a2', '2700.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3142, -1, 3927, -1, 8406, -1, 7299, -1], 'generators': [39916800, 5356806064, 43545600, 5872097345], 'label': '21600.y.900.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947533
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.g1.a1', '180.g1.b1', '300.g1.a1', '300.g1.b1', '450.c1.a1', '450.d1.a1', '450.d1.b1'], 'contains': ['1800.e1.a1', '1800.e1.b1', '1800.f1.a1', '1800.h1.a1', '1800.h1.b1', '1800.q1.a1', '1800.bd1.a1', '2700.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [7068, -1, 2914, -1, 7071, -1, 6904, -1], 'generators': [39916800, 5356806064, 43545600, 1680], 'label': '21600.y.900.h1.a1', 'mobius_quo': None, 'mobius_sub': 16, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947534
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.a1', '300.d1.a1', '300.e1.a1', '300.f1.a1', '450.d1.b1'], 'contains': ['1800.e1.a1', '1800.k1.a1', '1800.s1.a1', '2700.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3400, -1, 2596, -1, 6581, -1, 6855, -1], 'generators': [39916800, 43545600, 2424, 1680], 'label': '21600.y.900.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '900.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.i1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947535
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.b1', '300.d1.b1', '300.e1.b1', '300.f1.b1', '450.d1.a1'], 'contains': ['1800.e1.b1', '1800.k1.b1', '1800.s1.b1', '2700.c1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3400, -1, 8016, -1, 6581, -1, 6954, -1], 'generators': [39916800, 5356806064, 5872095665, 43545600], 'label': '21600.y.900.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '900.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.i1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947536
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.h1.a1', '450.c1.a1'], 'contains': ['1800.f1.a1', '1800.be1.a1', '1800.bf1.a1', '2700.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2181, -1, 6904, -1, 9374, -1, 7694, -1], 'generators': [5356808488, 39916800, 43545600, 5872097345], 'label': '21600.y.900.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a2', 'old_label': '900.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.j1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947537
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.h1.a2', '450.c1.a1'], 'contains': ['1800.f1.a1', '1800.be1.a2', '1800.bf1.a2', '2700.d1.a2'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2181, -1, 7408, -1, 9374, -1, 7892, -1], 'generators': [39916800, 5356806808, 43545600, 5872097345], 'label': '21600.y.900.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '900.j1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.j1.a2', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947538
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.e1.a1', '450.g1.b1'], 'contains': ['1800.h1.a1', '1800.l1.a1', '1800.n1.a1', '1800.bb1.a2', '1800.be1.a1', '1800.be1.a2', '2700.e1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [840, -1, 5311, -1, 8691, -1, 7645, -1], 'generators': [5875726145, 5316891688, 43545600, 1680], 'label': '21600.y.900.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947539
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.e1.a1', '450.g1.b1'], 'contains': ['1800.h1.a1', '1800.l1.a1', '1800.n1.a1', '1800.bb1.a1', '1800.be1.a1', '1800.be1.a2', '2700.e1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [840, -1, 5271, -1, 8691, -1, 7596, -1], 'generators': [5356808488, 5875726145, 43545600, 1680], 'label': '21600.y.900.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.k1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.k1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947540
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.e1.a1', '450.g1.a1'], 'contains': ['1800.h1.b1', '1800.l1.b1', '1800.n1.b1', '1800.bb1.b1', '1800.be1.a1', '1800.be1.a2', '2700.e1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [840, -1, 5490, -1, 8691, -1, 7744, -1], 'generators': [5875726145, 5316891688, 43545600, 39918480], 'label': '21600.y.900.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947541
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.e1.a1', '450.g1.a1'], 'contains': ['1800.h1.b1', '1800.l1.b1', '1800.n1.b1', '1800.bb1.b2', '1800.be1.a1', '1800.be1.a2', '2700.e1.b2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [840, -1, 5450, -1, 8691, -1, 7793, -1], 'generators': [5356808488, 5875726145, 43545600, 39918480], 'label': '21600.y.900.k1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.k1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.k1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947542
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '18.a1.a1'], 'contains': ['72.e1.b1', '180.a1.b1', '180.c1.b1', '216.a1.b1', '360.b1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [6999, -1, 4211, -1, 2742, -1, 1430, -1], 'generators': [39916800, 269671, 5352848792, 39927120], 'label': '21600.y.36.a1.b1', '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.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947543
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.i1.a1', '450.b1.b1'], 'contains': ['1800.g1.a1', '1800.i1.a1', '1800.m1.a1', '1800.ba1.b1', '1800.ba1.b2', '1800.bc1.b1', '2700.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2402, -1, 2308, -1, 6224, -1, 8787, -1], 'generators': [5352890793, 5832138543, 2424, 39918480], 'label': '21600.y.900.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '900.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947544
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.i1.b1', '450.b1.a1'], 'contains': ['1800.g1.b1', '1800.i1.b1', '1800.m1.b1', '1800.ba1.a1', '1800.ba1.a2', '1800.bc1.a1', '2700.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2402, -1, 7191, -1, 6224, -1, 9284, -1], 'generators': [4834223604, 4837857420, 1959914882, 4837847340], 'label': '21600.y.900.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '900.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947545
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.h1.a1', '300.i1.a1', '450.d1.b1', '450.e1.a1'], 'contains': ['1800.h1.a1', '1800.k1.a1', '1800.l1.a1', '1800.bb1.b1', '1800.bb1.b2', '1800.bd1.a1', '2700.f1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2783, -1, 2506, -1, 7519, -1, 7003, -1], 'generators': [43545600, 2424, 39918480, 5316889264], 'label': '21600.y.900.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.m1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947546
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.h1.b1', '300.i1.b1', '450.d1.a1', '450.e1.a1'], 'contains': ['1800.h1.b1', '1800.k1.b1', '1800.l1.b1', '1800.bb1.a1', '1800.bb1.a2', '1800.bd1.a1', '2700.f1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2783, -1, 3877, -1, 7519, -1, 7200, -1], 'generators': [5356806064, 43545600, 39918480, 5872097345], 'label': '21600.y.900.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947547
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.k1.b1', '300.n1.b1', '450.d1.a1', '450.e1.a1', '450.g1.b1'], 'contains': ['1800.h1.a1', '1800.k1.b1', '1800.n1.b1', '1800.q1.a1', '1800.bb1.a1', '1800.bb1.a2', '2700.g1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2283, -1, 6318, -1, 8500, -1, 7250, -1], 'generators': [43545600, 1680, 5316889264, 5872097345], 'label': '21600.y.900.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.n1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947548
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.k1.a1', '300.n1.a1', '450.d1.b1', '450.e1.a1', '450.g1.a1'], 'contains': ['1800.h1.b1', '1800.k1.a1', '1800.n1.a1', '1800.q1.a1', '1800.bb1.b1', '1800.bb1.b2', '2700.g1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2283, -1, 3120, -1, 8500, -1, 7151, -1], 'generators': [5356806064, 43545600, 2424, 39918480], 'label': '21600.y.900.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.n1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947549
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.g1.a1', '450.g1.b1'], 'contains': ['1800.n1.a1', '1800.n1.b1', '1800.q1.a1', '1800.be1.a1', '1800.be1.a2', '2700.h1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [759, -1, 6026, -1, 8835, -1, 7842, -1], 'generators': [5316891688, 43545600, 1680, 5872097345], 'label': '21600.y.900.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.o1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947550
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.e1.a1', '450.h1.a1'], 'contains': ['1800.l1.a1', '1800.l1.b1', '1800.q1.a1', '1800.bf1.a1', '1800.bf1.a2', '2700.i1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [399, -1, 6954, -1, 9147, -1, 7941, -1], 'generators': [5356808488, 43545600, 1680, 5872097345], 'label': '21600.y.900.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.p1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947551
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.o1.a1', '300.j1.a1', '300.k1.a1', '300.l1.a1', '450.a1.b1', '450.f1.b1'], 'contains': ['1800.u1.a1', '2700.j1.a1', '3600.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [4309, -1, 6566, -1, 5444, -1, 9023, -1], 'generators': [840, 2424, 1680, 5316889264], 'label': '21600.y.900.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '900.q1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947552
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.b1', '180.o1.b1', '300.j1.b1', '300.k1.b1', '300.l1.b1', '450.a1.a1', '450.f1.a1'], 'contains': ['1800.u1.b1', '2700.j1.b1', '3600.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [4309, -1, 6236, -1, 5444, -1, 8085, -1], 'generators': [5875726145, 5313260464, 83464080, 5875397673], 'label': '21600.y.900.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.b1', 'old_label': '900.q1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.q1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947553
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.b1', '15.a1.b1', '15.b1.b1', '20.a1.a1', '25.a1.a1', '30.b1.b1', '50.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3334, -1, 7461, -1, 5522, -1, 4305, -1], 'generators': [4877764140, 39916800, 43545600, 1963791510, 5396693366, 5392772192, 1959914882], 'label': '21600.y.5.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '5.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4320.ct'}
  • id: 63947554
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.b1.b1'], 'contains': ['72.a1.a1', '72.a1.b1', '72.b1.a1', '72.c1.a1', '72.c1.b1', '72.d1.a1', '72.f1.a1', '108.a1.a1', '180.g1.a1', '180.g1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8402, -1, 2157, -1, 743, -1, 813, -1], 'generators': [2043377285, 39916800, 43545600, 5832178862, 4837869084, 12360], 'label': '21600.y.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '36.b1.a1', 'projective_image': '21600.y', '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': '600.174'}
  • id: 63947555
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.j1.a1', '300.j1.a1', '300.m1.a1', '450.d1.b1', '450.g1.b1'], 'contains': ['1800.h1.a1', '1800.n1.a1', '1800.s1.a1', '2700.j1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3502, -1, 5769, -1, 8262, -1, 7102, -1], 'generators': [43545600, 2424, 1680, 5316889264], 'label': '21600.y.900.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '900.r1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.r1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947556
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.j1.b1', '300.j1.b1', '300.m1.b1', '450.d1.a1', '450.g1.a1'], 'contains': ['1800.h1.b1', '1800.n1.b1', '1800.s1.b1', '2700.j1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3502, -1, 8171, -1, 8262, -1, 7348, -1], 'generators': [5356806064, 5875726145, 43545600, 39918480], 'label': '21600.y.900.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '900.r1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.r1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947557
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.l1.a1', '300.m1.a1', '450.b1.b1'], 'contains': ['1800.i1.a1', '1800.o1.a1', '1800.t1.a1', '2700.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3042, -1, 5220, -1, 6793, -1, 8873, -1], 'generators': [5312973993, 5832138543, 2424, 1680], 'label': '21600.y.900.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.b1', 'old_label': '900.s1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.s1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947558
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.l1.b1', '300.m1.b1', '450.b1.a1'], 'contains': ['1800.i1.b1', '1800.o1.b1', '1800.t1.b1', '2700.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [3042, -1, 8760, -1, 6793, -1, 9383, -1], 'generators': [4834218540, 4834228620, 1959914882, 4837852404], 'label': '21600.y.900.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.a1.a1', 'old_label': '900.s1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.s1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947559
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.k1.a1', '300.m1.a1'], 'contains': ['1800.j1.a1', '1800.p1.a1', '1800.v1.a1', '2700.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [3582, -1, 6681, -1, 7165, -1, 5725, -1], 'generators': [5832138543, 2424, 5356519593, 1680], 'label': '21600.y.900.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.k1.a1', 'old_label': '900.t1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.t1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947560
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.k1.b1', '300.m1.b1'], 'contains': ['1800.j1.b1', '1800.p1.b1', '1800.v1.b1', '2700.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [3582, -1, 8908, -1, 7165, -1, 6524, -1], 'generators': [4834218540, 4877774220, 1959914882, 4837852404], 'label': '21600.y.900.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.k1.b1', 'old_label': '900.t1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.t1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947561
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.d1.a1', '300.n1.a1', '450.b1.b1'], 'contains': ['1800.g1.a1', '1800.o1.a1', '1800.r1.b1', '1800.z1.a1', '1800.ba1.b1', '1800.ba1.b2', '2700.g1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2484, -1, 2745, -1, 6319, -1, 8458, -1], 'generators': [5352890793, 2424, 39918480, 5792221743], 'label': '21600.y.900.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '900.u1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947562
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.d1.b1', '300.n1.b1', '450.b1.a1'], 'contains': ['1800.g1.b1', '1800.o1.b1', '1800.r1.a1', '1800.z1.b1', '1800.ba1.a1', '1800.ba1.a2', '2700.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2484, -1, 7664, -1, 6319, -1, 9186, -1], 'generators': [4837857420, 1959914882, 4837847340, 4837852404], 'label': '21600.y.900.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '900.u1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.u1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947563
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.l1.b1', '300.o1.a1', '300.p1.a1', '450.d1.a1', '450.g1.a1', '450.h1.a1'], 'contains': ['1800.l1.b1', '1800.q1.a1', '1800.s1.b1', '2700.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [961, -1, 7871, -1, 8596, -1, 7447, -1], 'generators': [5356806064, 43545600, 1680, 5872097345], 'label': '21600.y.900.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '900.v1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.v1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947564
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.l1.a1', '300.o1.b1', '300.p1.b1', '450.d1.b1', '450.g1.b1', '450.h1.a1'], 'contains': ['1800.l1.a1', '1800.q1.a1', '1800.s1.a1', '2700.k1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [961, -1, 6409, -1, 8596, -1, 7398, -1], 'generators': [5356806064, 43545600, 2424, 1680], 'label': '21600.y.900.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '900.v1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.v1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947565
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.b1'], 'contains': ['72.e1.a1', '180.i1.a1', '180.o1.a1', '216.c1.a1', '360.m1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7149, -1, 3692, -1, 2901, -1, 1650, -1], 'generators': [1963543685, 4837858860, 5792262062, 4837849524], 'label': '21600.y.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.c1.a1', 'projective_image': '21600.y', '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': '600.146'}
  • id: 63947566
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.m1.b1', '180.p1.a1', '300.o1.a1', '300.r1.a1', '450.a1.a1', '450.f1.a1', '450.i1.b1'], 'contains': ['1800.u1.b1', '2700.k1.a1', '3600.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1076, -1, 6271, -1, 6112, -1, 8128, -1], 'generators': [5791935273, 5313260464, 5792263745, 1680], 'label': '21600.y.900.w1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '900.w1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947567
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.m1.a1', '180.p1.b1', '300.o1.b1', '300.r1.b1', '450.a1.b1', '450.f1.b1', '450.i1.a1'], 'contains': ['1800.u1.a1', '2700.k1.b1', '3600.e1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1076, -1, 8448, -1, 6112, -1, 9127, -1], 'generators': [840, 5313260464, 2424, 1680], 'label': '21600.y.900.w1.b1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '900.w1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.w1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947568
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.n1.b1', '300.o1.a1', '300.q1.a1', '450.j1.a1'], 'contains': ['1800.w1.b1', '2700.k1.a1', '3600.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [144, -1, 9073, -1, 7607, -1, 4686, -1], 'generators': [5313260464, 5792263745, 1680, 5871768873], 'label': '21600.y.900.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.e1.b1', 'old_label': '900.x1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947569
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.n1.a1', '300.o1.b1', '300.q1.b1', '450.j1.b1'], 'contains': ['1800.w1.a1', '2700.k1.b1', '3600.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [144, -1, 9246, -1, 7607, -1, 6170, -1], 'generators': [5313260464, 2424, 79834440, 1680], 'label': '21600.y.900.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.e1.a1', 'old_label': '900.x1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.x1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947570
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.b1', '300.p1.a1', '300.q1.a1', '300.r1.a1', '450.b1.a1'], 'contains': ['1800.m1.b1', '1800.t1.b1', '1800.z1.b1', '2700.k1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [299, -1, 9479, -1, 7424, -1, 9334, -1], 'generators': [4834218540, 4834223604, 4834228620, 1959914882], 'label': '21600.y.900.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '900.y1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.y1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947571
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '300.p1.b1', '300.q1.b1', '300.r1.b1', '450.b1.b1'], 'contains': ['1800.m1.a1', '1800.t1.a1', '1800.z1.a1', '2700.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [299, -1, 5122, -1, 7424, -1, 8507, -1], 'generators': [5312973993, 2424, 1680, 5792221743], 'label': '21600.y.900.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '900.y1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.y1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 63947572
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.e1.a1'], 'contains': ['1800.bb1.a1', '1800.bb1.a2', '1800.bb1.b1', '1800.bb1.b2', '1800.bd1.a1', '1800.be1.a2', '1800.bf1.a1', '2700.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [560, -1, 3817, -1, 8930, -1, 7497, -1], 'generators': [5356808488, 43545600, 39918480, 5872097345], 'label': '21600.y.900.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.z1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947573
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '900.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '450.e1.a1'], 'contains': ['1800.bb1.a1', '1800.bb1.a2', '1800.bb1.b1', '1800.bb1.b2', '1800.bd1.a1', '1800.be1.a1', '1800.bf1.a2', '2700.l1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [560, -1, 3767, -1, 8930, -1, 7546, -1], 'generators': [5316891688, 43545600, 39918480, 5872097345], 'label': '21600.y.900.z1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '900.z1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.z1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947574
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '360.b1.a1', '360.e1.a1', '540.a1.a1', '540.b1.a1', '540.c1.a1'], 'contains': ['2160.a1.a1', '2160.c1.a1', '2160.e1.b1', '5400.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7664, -1, 946, -1, 2048, -1, 2143, -1], 'generators': [39916800, 1680, 5792223420], 'label': '21600.y.1080.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947575
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.b1', '360.b1.b1', '360.e1.b1', '540.a1.b1', '540.b1.b1', '540.c1.b1'], 'contains': ['2160.a1.b1', '2160.c1.b1', '2160.e1.a1', '5400.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7664, -1, 1071, -1, 2048, -1, 4184, -1], 'generators': [4834218540, 83468400, 83462400], 'label': '21600.y.1080.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947576
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.a1.a1'], 'contains': ['72.e1.b1', '180.i1.b1', '180.o1.b1', '216.c1.b1', '360.m1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7149, -1, 4380, -1, 2901, -1, 1383, -1], 'generators': [10320, 83732815, 83467560, 5312931992], 'label': '21600.y.36.c1.b1', '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.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
  • id: 63947577
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '216.a1.a1', '360.c1.a1', '360.f1.a1', '540.c1.b1'], 'contains': ['2160.a1.b1', '2160.d1.a1', '2160.f1.b1', '5400.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7191, -1, 728, -1, 1453, -1, 4032, -1], 'generators': [17520, 83468400, 83462400], 'label': '21600.y.1080.b1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '1080.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947578
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.b1', '216.a1.b1', '360.c1.b1', '360.f1.b1', '540.c1.a1'], 'contains': ['2160.a1.a1', '2160.d1.b1', '2160.f1.a1', '5400.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7191, -1, 1309, -1, 1453, -1, 1991, -1], 'generators': [39916800, 4834258861, 5792221740], 'label': '21600.y.1080.b1.b1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '1080.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.b1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947579
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.d1.a1', '360.g1.a1', '540.a1.a1', '540.c1.a1'], 'contains': ['2160.a1.a1', '2160.g1.a1', '2160.i1.a1', '5400.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [8899, -1, 3241, -1, 2468, -1, 2075, -1], 'generators': [39916800, 4834260541, 5792221740], 'label': '21600.y.1080.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947580
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '360.d1.b1', '360.g1.b1', '540.a1.b1', '540.c1.b1'], 'contains': ['2160.a1.b1', '2160.g1.b1', '2160.i1.b1', '5400.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [8899, -1, 3264, -1, 2468, -1, 4116, -1], 'generators': [83468400, 5396700062, 83462400], 'label': '21600.y.1080.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947581
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.a1', '216.b1.a1', '360.h1.a1'], 'contains': ['2160.b1.a1', '2160.h1.a1', '2160.j1.a1', '5400.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [9704, -1, 3218, -1, 3920, -1, 2541, -1], 'generators': [3628800, 4837869084, 4833942753], 'label': '21600.y.1080.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.d1.a1', 'old_label': '1080.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947582
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.b1', '216.b1.a1', '360.h1.b1'], 'contains': ['2160.b1.b1', '2160.h1.b1', '2160.j1.b1', '5400.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [9704, -1, 3425, -1, 3920, -1, 2695, -1], 'generators': [5795903222, 3628800, 4837869084], 'label': '21600.y.1080.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.d1.b1', 'old_label': '1080.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947583
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.i1.a1', '540.b1.a1', '540.d1.a1', '540.f1.a1'], 'contains': ['2160.c1.a1', '2160.e1.b1', '5400.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4771, -1, 2398, -1, 3327, -1, 2279, -1], 'generators': [2424, 39918480, 5832140220], 'label': '21600.y.1080.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947584
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.i1.b1', '540.b1.b1', '540.d1.b1', '540.f1.b1'], 'contains': ['2160.c1.b1', '2160.e1.a1', '5400.d1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4771, -1, 5504, -1, 3327, -1, 4320, -1], 'generators': [4834218540, 2043377282, 2043383282], 'label': '21600.y.1080.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947585
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '360.j1.a1', '360.m1.a1', '540.c1.a1', '540.d1.a1', '540.e1.a1'], 'contains': ['2160.c1.a1', '2160.f1.a1', '2160.i1.a1', '5400.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7766, -1, 2624, -1, 2522, -1, 2103, -1], 'generators': [1680, 4917721261, 5792223420], 'label': '21600.y.1080.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.f1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947586
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.b1', '360.j1.b1', '360.m1.b1', '540.c1.b1', '540.d1.b1', '540.e1.b1'], 'contains': ['2160.c1.b1', '2160.f1.b1', '2160.i1.b1', '5400.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7766, -1, 1678, -1, 2522, -1, 4144, -1], 'generators': [6000, 4834218540, 4837864860], 'label': '21600.y.1080.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.f1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947587
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '12.c1.a1', '18.a1.a1'], 'contains': ['72.e1.b1', '180.m1.b1', '180.p1.a1', '216.d1.a1', '360.u1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2148, -1, 5442, -1, 3133, -1, 1477, -1], 'generators': [5160, 10320, 270415, 5312931992], 'label': '21600.y.36.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.d1.a1', 'projective_image': '21600.y', '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': '600.146'}
  • id: 63947588
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.k1.a1', '540.a1.a1', '540.d1.a1', '540.g1.a1'], 'contains': ['2160.c1.a1', '2160.g1.a1', '5400.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4461, -1, 4760, -1, 3481, -1, 2347, -1], 'generators': [1680, 4834261285, 5792223420], 'label': '21600.y.1080.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '1080.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.g1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947589
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.k1.b1', '540.a1.b1', '540.d1.b1', '540.g1.b1'], 'contains': ['2160.c1.b1', '2160.g1.b1', '5400.e1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4461, -1, 5569, -1, 3481, -1, 4388, -1], 'generators': [6000, 4834218540, 5313237662], 'label': '21600.y.1080.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '1080.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.g1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947590
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.a1', '540.a1.a1', '540.e1.a1', '540.f1.a1'], 'contains': ['2160.c1.a1', '2160.i1.a1', '5400.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4415, -1, 3527, -1, 3404, -1, 2319, -1], 'generators': [4917723685, 1680, 5792223420], 'label': '21600.y.1080.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.h1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947591
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.b1', '540.a1.b1', '540.e1.b1', '540.f1.b1'], 'contains': ['2160.c1.b1', '2160.i1.b1', '5400.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4415, -1, 5536, -1, 3404, -1, 4360, -1], 'generators': [6000, 4834218540, 5396700062], 'label': '21600.y.1080.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.h1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947592
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.a1', '360.o1.a1', '360.p1.a1', '540.b1.a1', '540.e1.a1', '540.g1.a1'], 'contains': ['2160.c1.a1', '5400.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5152, -1, 5739, -1, 4087, -1, 2387, -1], 'generators': [2424, 1680, 5792223420], 'label': '21600.y.1080.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '1080.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947593
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.b1', '360.o1.b1', '360.p1.b1', '540.b1.b1', '540.e1.b1', '540.g1.b1'], 'contains': ['2160.c1.b1', '5400.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5152, -1, 7370, -1, 4087, -1, 4428, -1], 'generators': [4834218540, 1959914882, 1959920882], 'label': '21600.y.1080.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '1080.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947594
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '216.c1.a1', '360.q1.a1', '360.r1.a1', '360.s1.a1', '540.c1.b1', '540.f1.b1'], 'contains': ['2160.d1.a1', '2160.e1.a1', '2160.i1.b1', '5400.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [6296, -1, 1655, -1, 2223, -1, 4060, -1], 'generators': [6000, 4837864860, 4837847340], 'label': '21600.y.1080.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.j1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947595
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.b1', '216.c1.b1', '360.q1.b1', '360.r1.b1', '360.s1.b1', '540.c1.a1', '540.f1.a1'], 'contains': ['2160.d1.b1', '2160.e1.b1', '2160.i1.a1', '5400.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [6296, -1, 3011, -1, 2223, -1, 2019, -1], 'generators': [4834258861, 39918480, 5832140220], 'label': '21600.y.1080.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.j1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947596
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.p1.a1', '216.d1.a1', '360.t1.a1', '360.u1.a1', '540.c1.a1', '540.f1.a1', '540.g1.a1'], 'contains': ['2160.c1.a1', '2160.d1.b1', '2160.g1.a1', '5400.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [1766, -1, 5010, -1, 3251, -1, 2183, -1], 'generators': [4834258861, 1680, 5792223420], 'label': '21600.y.1080.k1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '1080.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.k1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947597
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.p1.b1', '216.d1.a1', '360.t1.b1', '360.u1.b1', '540.c1.b1', '540.f1.b1', '540.g1.b1'], 'contains': ['2160.c1.b1', '2160.d1.a1', '2160.g1.b1', '5400.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [1766, -1, 4900, -1, 3251, -1, 4224, -1], 'generators': [6000, 4834218540, 4834236060], 'label': '21600.y.1080.k1.b1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '1080.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.k1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947598
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '12.c1.b1', '18.a1.b1'], 'contains': ['72.e1.a1', '180.m1.a1', '180.p1.b1', '216.d1.a1', '360.u1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2148, -1, 5213, -1, 3133, -1, 1607, -1], 'generators': [1959914885, 5792262062, 4834230060, 4834220724], 'label': '21600.y.36.d1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '36.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
  • id: 63947599
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.a1', '540.a1.b1', '540.d1.b1', '540.f1.b1'], 'contains': ['2160.e1.a1', '2160.g1.b1', '2160.i1.b1', '5400.i1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4646, -1, 1816, -1, 3015, -1, 4252, -1], 'generators': [6000, 4917680940, 5396700062], 'label': '21600.y.1080.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.l1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947600
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.a2', '540.a1.b1', '540.d1.b1', '540.f1.b1'], 'contains': ['2160.e1.a1', '2160.g1.b1', '2160.i1.b1', '5400.i1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4646, -1, 1947, -1, 3015, -1, 4280, -1], 'generators': [6000, 5313237662, 4837847340], 'label': '21600.y.1080.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.l1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.l1.a2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947601
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.b1', '540.a1.a1', '540.d1.a1', '540.f1.a1'], 'contains': ['2160.e1.b1', '2160.g1.a1', '2160.i1.a1', '5400.i1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4646, -1, 1970, -1, 3015, -1, 2211, -1], 'generators': [83464080, 4917723685, 5875685820], 'label': '21600.y.1080.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.l1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947602
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.b2', '540.a1.a1', '540.d1.a1', '540.f1.a1'], 'contains': ['2160.e1.b1', '2160.g1.a1', '2160.i1.a1', '5400.i1.b2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [4646, -1, 2032, -1, 3015, -1, 2239, -1], 'generators': [39918480, 4834261285, 5832140220], 'label': '21600.y.1080.l1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.l1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.l1.b2', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947603
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '360.w1.a1', '360.x1.a1', '540.c1.b1', '540.d1.b1'], 'contains': ['2160.e1.a1', '2160.f1.b1', '2160.g1.b1', '5400.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [8413, -1, 1009, -1, 1672, -1, 4088, -1], 'generators': [6000, 4837847340, 4834236060], 'label': '21600.y.1080.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '1080.m1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.m1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947604
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1080.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '360.w1.b1', '360.x1.b1', '540.c1.a1', '540.d1.a1'], 'contains': ['2160.e1.b1', '2160.f1.a1', '2160.g1.a1', '5400.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [8413, -1, 1514, -1, 1672, -1, 2047, -1], 'generators': [83464080, 4917721261, 5875685820], 'label': '21600.y.1080.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '1080.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.m1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947605
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.a1.a1', '300.a1.b1', '400.a1.a1', '600.a1.a1', '600.a1.b1', '600.b1.a1'], 'contains': ['2400.d1.a1', '3600.b1.a1', '3600.b1.b1', '3600.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [3815, -1, 5932, -1, 7211, -1, 7641, -1], 'generators': [83462640, 5875396137, 83462400], 'label': '21600.y.1200.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '1200.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947606
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '300.e1.a1', '400.a1.a1', '600.c1.b1', '600.d1.a1', '600.e1.a1'], 'contains': ['2400.a1.a1', '3600.a1.a1', '3600.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6453, -1, 4490, -1, 5397, -1, 5952, -1], 'generators': [39916800, 43545600, 83463240], 'label': '21600.y.1200.b1.a1', 'mobius_quo': None, 'mobius_sub': -120, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '1200.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947607
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.b1', '300.e1.b1', '400.a1.a1', '600.c1.a1', '600.d1.b1', '600.e1.b1'], 'contains': ['2400.a1.b1', '3600.a1.a1', '3600.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6453, -1, 948, -1, 5397, -1, 5179, -1], 'generators': [39916800, 5875395993, 43545600], 'label': '21600.y.1200.b1.b1', 'mobius_quo': None, 'mobius_sub': -120, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '1200.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947608
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.f1.a1', '300.f1.b1', '300.h1.a1', '300.h1.a2', '400.a1.a1', '600.f1.a1'], 'contains': ['2400.b1.a1', '3600.a1.a1', '3600.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [3962, -1, 6769, -1, 8354, -1, 6661, -1], 'generators': [39916800, 43545600, 5875396137], 'label': '21600.y.1200.c1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.b1.a1', 'old_label': '1200.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947609
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '20.a1.a1', '20.b1.a1', '20.c1.b1'], 'contains': ['120.a1.a1', '120.i1.a1', '120.j1.a1', '200.d1.a1', '240.c1.a1', '400.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2582, -1, 8232, -1, 5013, -1, 3821, -1], 'generators': [43545600, 79844424, 5392772192, 5312931992], 'label': '21600.y.40.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '40.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '240.190'}
  • id: 63947610
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.a1', '300.o1.a1', '400.b1.a1', '600.c1.a1', '600.g1.a1', '600.h1.a1', '600.i1.a1', '600.j1.a1', '600.n1.a1', '600.u1.a1'], 'contains': ['2400.a1.b1', '3600.d1.a1', '3600.e1.a1', '3600.f1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [1909, -1, 3163, -1, 6113, -1, 5418, -1], 'generators': [43545600, 1680, 5871768873], 'label': '21600.y.1200.d1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '1200.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947611
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.b1', '300.o1.b1', '400.b1.b1', '600.c1.b1', '600.g1.b1', '600.h1.b1', '600.i1.b1', '600.j1.b1', '600.n1.b1', '600.u1.b1'], 'contains': ['2400.a1.a1', '3600.d1.b1', '3600.e1.b1', '3600.f1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [1909, -1, 9022, -1, 6113, -1, 6165, -1], 'generators': [5356806064, 43545600, 79834440], 'label': '21600.y.1200.d1.b1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '1200.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947612
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '240.b1.a1', '400.b1.a1', '600.d1.a1', '600.k1.a1', '600.u1.b1'], 'contains': ['2400.a1.a1', '3600.d1.a1', '3600.g1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5406, -1, 7962, -1, 5232, -1, 5881, -1], 'generators': [43545600, 79843680, 79838664], 'label': '21600.y.1200.e1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '1200.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947613
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.b1', '240.b1.b1', '400.b1.b1', '600.d1.b1', '600.k1.b1', '600.u1.a1'], 'contains': ['2400.a1.b1', '3600.d1.b1', '3600.g1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5406, -1, 5725, -1, 5232, -1, 4795, -1], 'generators': [43545600, 5312972313, 5792221743], 'label': '21600.y.1200.e1.b1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '1200.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947614
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.a1', '300.q1.a1', '400.b1.a1', '600.l1.a1'], 'contains': ['2400.c1.a1', '3600.f1.a1', '3600.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [2176, -1, 8065, -1, 5546, -1, 5469, -1], 'generators': [43843830, 43833750, 5064], 'label': '21600.y.1200.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.c1.a1', 'old_label': '1200.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947615
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.i1.b1', '300.q1.b1', '400.b1.b1', '600.l1.b1'], 'contains': ['2400.c1.b1', '3600.f1.b1', '3600.g1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [2176, -1, 9596, -1, 5546, -1, 6008, -1], 'generators': [79833840, 5792221743, 5392806153], 'label': '21600.y.1200.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.c1.b1', 'old_label': '1200.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947616
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.j1.a1', '300.r1.a1', '400.b1.a1', '600.a1.a1', '600.m1.a1', '600.v1.a1'], 'contains': ['2400.d1.a1', '3600.e1.a1', '3600.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3232, -1, 8100, -1, 5672, -1, 7447, -1], 'generators': [298230, 288150, 5064], 'label': '21600.y.1200.g1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '1200.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947617
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.j1.b1', '300.r1.b1', '400.b1.b1', '600.a1.b1', '600.m1.b1', '600.v1.a1'], 'contains': ['2400.d1.a1', '3600.e1.b1', '3600.g1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3232, -1, 8618, -1, 5672, -1, 7336, -1], 'generators': [5312972553, 240, 5792221743], 'label': '21600.y.1200.g1.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '1200.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947618
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.e1.a1', '300.j1.a1', '400.c1.a1', '600.c1.b1', '600.g1.b1', '600.k1.a1', '600.w1.a1', '600.w1.a2', '600.y1.a1'], 'contains': ['2400.a1.a1', '3600.h1.a1', '3600.i1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4795, -1, 6512, -1, 5083, -1, 6050, -1], 'generators': [43545600, 79834440, 5316889264], 'label': '21600.y.1200.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '1200.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947619
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.e1.b1', '300.j1.b1', '400.c1.b1', '600.c1.a1', '600.g1.a1', '600.k1.b1', '600.w1.b1', '600.w1.b2', '600.y1.b1'], 'contains': ['2400.a1.b1', '3600.h1.b1', '3600.i1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4795, -1, 1261, -1, 5083, -1, 5293, -1], 'generators': [43545600, 39918480, 5875397673], 'label': '21600.y.1200.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '1200.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947620
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '20.a1.b1', '20.b1.b1', '20.c1.a1'], 'contains': ['120.a1.b1', '120.i1.b1', '120.j1.b1', '200.d1.b1', '240.c1.b1', '400.b1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [2582, -1, 7728, -1, 5013, -1, 2054, -1], 'generators': [79833840, 5313220382, 43545600, 5835519751], 'label': '21600.y.40.a1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '240.190'}
  • id: 63947621
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.k1.a1', '400.c1.a1', '600.l1.a1'], 'contains': ['2400.c1.a1', '3600.h1.a1', '3600.k1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [5055, -1, 6695, -1, 4807, -1, 5560, -1], 'generators': [5832138543, 240, 5392806153], 'label': '21600.y.1200.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.l1.a1', 'old_label': '1200.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947622
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.k1.b1', '400.c1.b1', '600.l1.b1'], 'contains': ['2400.c1.b1', '3600.h1.b1', '3600.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [5055, -1, 7550, -1, 4807, -1, 6220, -1], 'generators': [43843830, 83467464, 288150], 'label': '21600.y.1200.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.l1.b1', 'old_label': '1200.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947623
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.l1.a1', '400.c1.a1', '600.a1.b1', '600.m1.a1', '600.x1.a1'], 'contains': ['2400.d1.a1', '3600.h1.a1', '3600.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4886, -1, 6475, -1, 4933, -1, 7526, -1], 'generators': [5312972553, 5832138543, 240], 'label': '21600.y.1200.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '1200.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947624
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.l1.b1', '400.c1.b1', '600.a1.a1', '600.m1.b1', '600.x1.a1'], 'contains': ['2400.d1.a1', '3600.h1.b1', '3600.j1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4886, -1, 5103, -1, 4933, -1, 7569, -1], 'generators': [298230, 83467464, 288150], 'label': '21600.y.1200.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '1200.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947625
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '400.c1.a1', '600.d1.b1', '600.h1.a1', '600.y1.b1'], 'contains': ['2400.a1.b1', '3600.i1.a1', '3600.j1.a1', '3600.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6728, -1, 1423, -1, 4739, -1, 5258, -1], 'generators': [43545600, 5832138543, 5312972313], 'label': '21600.y.1200.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '1200.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947626
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.b1', '400.c1.b1', '600.d1.a1', '600.h1.b1', '600.y1.a1'], 'contains': ['2400.a1.a1', '3600.i1.b1', '3600.j1.b1', '3600.k1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6728, -1, 6657, -1, 4739, -1, 5917, -1], 'generators': [43545600, 83467464, 79843680], 'label': '21600.y.1200.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '1200.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.k1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947627
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.f1.a1', '400.d1.a1', '600.e1.a1', '600.i1.b1', '600.u1.b1', '600.w1.a1', '600.w1.a2', '600.y1.a1'], 'contains': ['2400.a1.a1', '3600.l1.a1', '3600.m1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6298, -1, 8530, -1, 6196, -1, 6122, -1], 'generators': [4877769204, 43545600, 79843680], 'label': '21600.y.1200.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '1200.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947628
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.f1.b1', '400.d1.a1', '600.e1.b1', '600.i1.a1', '600.u1.a1', '600.w1.b1', '600.w1.b2', '600.y1.b1'], 'contains': ['2400.a1.b1', '3600.l1.a1', '3600.m1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6298, -1, 4216, -1, 6196, -1, 5371, -1], 'generators': [43545600, 5792223423, 5312972313], 'label': '21600.y.1200.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '1200.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947629
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.l1.a1', '120.l1.b1', '400.d1.a1', '600.f1.a1'], 'contains': ['2400.b1.a1', '3600.l1.a1', '3600.n1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [6523, -1, 9561, -1, 8530, -1, 6461, -1], 'generators': [43545600, 15988, 1959931561], 'label': '21600.y.1200.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.f1.a1', 'old_label': '1200.m1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63947630
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['400.d1.a1', '600.b1.a1', '600.v1.a1', '600.x1.a1'], 'contains': ['2400.d1.a1', '3600.m1.a1', '3600.m1.b1', '3600.n1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6582, -1, 8647, -1, 7093, -1, 7722, -1], 'generators': [15988, 1959931561, 15984], 'label': '21600.y.1200.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '1200.n1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947631
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.b1.a1'], 'contains': ['90.b1.a1', '90.d1.a1', '90.e1.a1', '225.a1.b1', '270.a1.a1', '450.b1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [3408, -1, 4852, -1, 5529, -1, 2791, -1], 'generators': [5791975591, 5396684222, 2424, 1680, 83462400], 'label': '21600.y.45.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '21600.y', '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': '180.19'}
  • id: 63947632
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.a1', '400.e1.a1', '600.e1.a1', '600.h1.b1', '600.j1.b1', '600.k1.a1', '600.w1.a1', '600.w1.a2'], 'contains': ['2400.a1.a1', '3600.o1.a1', '3600.p1.a1', '3600.q1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6086, -1, 7722, -1, 6044, -1, 6086, -1], 'generators': [43545600, 79843680, 4837852404], 'label': '21600.y.1200.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '1200.o1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.o1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947633
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.g1.b1', '400.e1.a1', '600.e1.b1', '600.h1.a1', '600.j1.a1', '600.k1.b1', '600.w1.b1', '600.w1.b2'], 'contains': ['2400.a1.b1', '3600.o1.a1', '3600.p1.b1', '3600.q1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6086, -1, 1800, -1, 6044, -1, 5335, -1], 'generators': [43545600, 5832140223, 5312972313], 'label': '21600.y.1200.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '1200.o1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.o1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947634
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['400.e1.a1', '600.f1.a1'], 'contains': ['2400.b1.a1', '3600.o1.a1', '3600.r1.a1', '3600.s1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [7408, -1, 8569, -1, 8168, -1, 6591, -1], 'generators': [43545600, 15988, 1999848361], 'label': '21600.y.1200.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.f1.a1', 'old_label': '1200.p1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.p1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947635
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['400.e1.a1', '600.l1.a1'], 'contains': ['2400.c1.a1', '3600.p1.a1', '3600.q1.a1', '3600.s1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [5835, -1, 8140, -1, 6536, -1, 5624, -1], 'generators': [1999848361, 15984, 79849588], 'label': '21600.y.1200.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.l1.a1', 'old_label': '1200.q1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.q1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947636
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['400.e1.a1', '600.l1.b1'], 'contains': ['2400.c1.b1', '3600.p1.b1', '3600.q1.b1', '3600.s1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [5835, -1, 8280, -1, 6536, -1, 6255, -1], 'generators': [79849584, 1999848361, 79849588], 'label': '21600.y.1200.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.l1.b1', 'old_label': '1200.q1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.q1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947637
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['400.e1.a1', '600.b1.a1', '600.m1.a1', '600.m1.b1'], 'contains': ['2400.d1.a1', '3600.p1.a1', '3600.p1.b1', '3600.r1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [6163, -1, 7781, -1, 7038, -1, 7605, -1], 'generators': [15988, 1999848361, 15984], 'label': '21600.y.1200.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a1', 'old_label': '1200.r1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.r1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 63947638
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1200.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['400.e1.a1'], 'contains': ['2400.e1.a1', '3600.q1.a1', '3600.q1.b1', '3600.r1.a1', '3600.s1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1200, 'diagramx': [6375, -1, 8344, -1, 8063, -1, 5595, -1], 'generators': [79849584, 15988, 1999848361], 'label': '21600.y.1200.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1200.s1.a1', 'old_label': '1200.s1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.s1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 63947639
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1350.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.c1.a1', '675.a1.a1'], 'contains': ['2700.a1.a1', '2700.a1.b1', '2700.b1.a1', '2700.d1.a1', '2700.d1.a2', '2700.e1.a1', '2700.e1.a2', '2700.e1.b1', '2700.e1.b2', '2700.h1.a1', '2700.i1.a1', '2700.l1.a1', '2700.l1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [729, -1, 6929, -1, 9075, -1, 9964, -1], 'generators': [39916800, 5792263745, 1680, 5313262888], 'label': '21600.y.1350.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '1350.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947640
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1350.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.a1.b1', '450.a1.a1', '450.b1.a1', '450.d1.a1', '675.a1.a1'], 'contains': ['2700.a1.b1', '2700.b1.a1', '2700.c1.b1', '2700.f1.b1', '2700.g1.a1', '2700.j1.b1', '2700.k1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3524, -1, 7445, -1, 8334, -1, 9860, -1], 'generators': [39916800, 5313260464, 5792263745, 1680], 'label': '21600.y.1350.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.b1', 'old_label': '1350.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947641
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1350.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['270.a1.a1', '450.a1.b1', '450.b1.b1', '450.d1.b1', '675.a1.a1'], 'contains': ['2700.a1.a1', '2700.b1.a1', '2700.c1.a1', '2700.f1.a1', '2700.g1.b1', '2700.j1.a1', '2700.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3524, -1, 4430, -1, 8334, -1, 9834, -1], 'generators': [39916800, 5313260464, 2424, 1680], 'label': '21600.y.1350.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '1350.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.b1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947642
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '15.b1.b1'], 'contains': ['90.b1.b1', '90.d1.b1', '90.e1.b1', '225.a1.a1', '270.a1.b1', '450.b1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3408, -1, 7428, -1, 5529, -1, 4515, -1], 'generators': [5396689142, 4834218540, 5396693366, 1959914882, 83462400], 'label': '21600.y.45.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '45.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.b1', 'subgroup_fusion': None, 'weyl_group': '180.19'}
  • id: 63947643
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1350.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.e1.a1', '675.a1.a1'], 'contains': ['2700.e1.a1', '2700.e1.a2', '2700.e1.b1', '2700.e1.b2', '2700.f1.a1', '2700.f1.b1', '2700.g1.a1', '2700.g1.b1', '2700.i1.a1', '2700.l1.a1', '2700.l1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [483, -1, 6836, -1, 9025, -1, 9990, -1], 'generators': [5313260464, 5792263745, 2424, 39918480], 'label': '21600.y.1350.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '1350.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947644
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1350.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.f1.a1', '450.g1.a1', '675.a1.a1'], 'contains': ['2700.e1.b1', '2700.e1.b2', '2700.g1.b1', '2700.h1.a1', '2700.j1.b1', '2700.k1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [956, -1, 7509, -1, 8763, -1, 9886, -1], 'generators': [5875726145, 5313260464, 83464080, 2424], 'label': '21600.y.1350.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.b1', 'old_label': '1350.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947645
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1350.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.f1.b1', '450.g1.b1', '675.a1.a1'], 'contains': ['2700.e1.a1', '2700.e1.a2', '2700.g1.a1', '2700.h1.a1', '2700.j1.a1', '2700.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [956, -1, 7164, -1, 8763, -1, 9912, -1], 'generators': [5792263745, 2424, 1680, 5316889264], 'label': '21600.y.1350.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '1350.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.d1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947646
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1350.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.h1.a1', '450.i1.a1', '450.i1.b1', '450.j1.a1', '450.j1.b1', '450.k1.a1', '450.k1.a2', '450.l1.a1', '450.l1.a2', '675.a1.a1'], 'contains': ['2700.i1.a1', '2700.k1.a1', '2700.k1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [38, -1, 9364, -1, 9598, -1, 9938, -1], 'generators': [5313260464, 5792263745, 2424, 1680], 'label': '21600.y.1350.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '1350.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1350.e1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 63947647
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '480.a1.a1', '720.b1.a1', '720.d1.a1', '720.f1.b1', '720.i1.b1', '720.m1.a1', '720.n1.a1', '720.q1.a1'], 'contains': ['4320.a1.a1', '7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8071, -1, 973, -1, 2339, -1, 1215, -1], 'generators': [43545600, 5792221740], 'label': '21600.y.1440.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '1440.a1.a1', 'projective_image': '21600.y', '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': '4.2'}
  • id: 63947648
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '480.a1.b1', '720.b1.b1', '720.d1.b1', '720.f1.a1', '720.i1.a1', '720.m1.b1', '720.n1.b1', '720.q1.b1'], 'contains': ['4320.a1.b1', '7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8071, -1, 658, -1, 2339, -1, 3246, -1], 'generators': [43545600, 79839600], 'label': '21600.y.1440.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '1440.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947649
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '720.c1.a1', '720.o1.a1', '720.r1.a1'], 'contains': ['4320.b1.a1', '7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9829, -1, 862, -1, 3866, -1, 2463, -1], 'generators': [43545600, 4913776353], 'label': '21600.y.1440.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '1440.b1.a1', 'projective_image': '21600.y', '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': '4.2'}
  • id: 63947650
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '720.c1.b1', '720.o1.b1', '720.r1.b1'], 'contains': ['4320.b1.b1', '7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9829, -1, 696, -1, 3866, -1, 2617, -1], 'generators': [43545600, 5792274422], 'label': '21600.y.1440.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '1440.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947651
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.o1.a1', '480.a1.a1', '720.a1.a1', '720.e1.a1', '720.g1.b1', '720.j1.b1', '720.l1.a1', '720.p1.a1', '720.s1.a1'], 'contains': ['4320.a1.a1', '7200.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8545, -1, 4537, -1, 2393, -1, 1859, -1], 'generators': [240, 5792221980], 'label': '21600.y.1440.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '1440.c1.a1', 'projective_image': '21600.y', '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': '4.2'}
  • id: 63947652
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.o1.b1', '480.a1.b1', '720.a1.b1', '720.e1.b1', '720.g1.a1', '720.j1.a1', '720.l1.b1', '720.p1.b1', '720.s1.b1'], 'contains': ['4320.a1.b1', '7200.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8545, -1, 635, -1, 2393, -1, 3892, -1], 'generators': [6000, 1960162710], 'label': '21600.y.1440.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '1440.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947653
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1', '10.a1.a1'], 'contains': ['100.a1.b1', '100.c1.b1', '100.d1.a1', '150.a1.a1', '150.b1.a1', '150.c1.a1', '200.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3307, -1, 7906, -1, 5751, -1, 4776, -1], 'generators': [4877764140, 39916800, 43545600, 1963791510, 1959914882, 40215030, 4837852404], 'label': '21600.y.50.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '50.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.749'}
  • id: 63947654
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.p1.b1', '480.a1.b1', '720.h1.a1', '720.k1.a1', '720.t1.a1'], 'contains': ['4320.a1.b1', '7200.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7191, -1, 3921, -1, 2446, -1, 3687, -1], 'generators': [6000, 2003708310], 'label': '21600.y.1440.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1.a1', 'old_label': '1440.d1.a1', 'projective_image': '21600.y', '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': '4.2'}
  • id: 63947655
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1440.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.p1.a1', '480.a1.a1', '720.h1.b1', '720.k1.b1', '720.t1.b1'], 'contains': ['4320.a1.a1', '7200.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7191, -1, 5064, -1, 2446, -1, 1646, -1], 'generators': [5872055580, 79833840], 'label': '21600.y.1440.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.g1.b1', 'old_label': '1440.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947656
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.a1', '450.a1.a1', '600.a1.a1', '600.c1.a1', '900.a1.a1', '900.b1.a1', '900.e1.a1'], 'contains': ['3600.b1.b1', '3600.e1.a1', '3600.h1.b1', '5400.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [4072, -1, 1905, -1, 5315, -1, 7758, -1], 'generators': [1680, 5875397673, 83462400], 'label': '21600.y.1800.a1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947657
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.b1', '450.a1.b1', '600.a1.b1', '600.c1.b1', '900.a1.b1', '900.b1.b1', '900.e1.b1'], 'contains': ['3600.b1.a1', '3600.e1.b1', '3600.h1.a1', '5400.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [4072, -1, 4815, -1, 5315, -1, 8209, -1], 'generators': [5313260464, 83463240, 83462400], 'label': '21600.y.1800.a1.b1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947658
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '360.b1.a1', '600.a1.a1', '600.d1.a1', '900.e1.b1'], 'contains': ['3600.b1.a1', '3600.g1.a1', '3600.j1.b1', '5400.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6801, -1, 4719, -1, 4871, -1, 7972, -1], 'generators': [83467464, 83472480, 83462400], 'label': '21600.y.1800.b1.a1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '1800.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947659
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.b1', '360.b1.b1', '600.a1.b1', '600.d1.b1', '900.e1.a1'], 'contains': ['3600.b1.b1', '3600.g1.b1', '3600.j1.a1', '5400.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6801, -1, 1868, -1, 4871, -1, 7369, -1], 'generators': [39916800, 5352889113, 5792221743], 'label': '21600.y.1800.b1.b1', 'mobius_quo': None, 'mobius_sub': -60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '1800.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947660
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.d1.a1', '600.b1.a1', '600.e1.a1', '900.a1.b1', '900.e1.b1'], 'contains': ['3600.b1.a1', '3600.m1.a1', '3600.p1.a1', '5400.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [7142, -1, 4788, -1, 5995, -1, 8118, -1], 'generators': [3628800, 4837852404, 3638880], 'label': '21600.y.1800.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947661
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.d1.b1', '600.b1.a1', '600.e1.b1', '900.a1.a1', '900.e1.a1'], 'contains': ['3600.b1.b1', '3600.m1.b1', '3600.p1.b1', '5400.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [7142, -1, 3529, -1, 5995, -1, 7674, -1], 'generators': [39916800, 5352889113, 5792223423], 'label': '21600.y.1800.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947662
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.a1', '180.d1.b1', '600.b1.a1', '600.f1.a1'], 'contains': ['3600.c1.a1', '3600.n1.a1', '3600.r1.a1', '5400.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1800, 'diagramx': [8908, -1, 7752, -1, 8268, -1, 8545, -1], 'generators': [39916800, 15988, 1959931561], 'label': '21600.y.1800.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1800.d1.a1', 'old_label': '1800.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947663
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.e1.a1', '360.f1.a1', '600.c1.a1', '600.d1.a1', '900.g1.a1', '900.h1.a1', '900.i1.a1'], 'contains': ['3600.a1.a1', '3600.d1.a1', '3600.i1.b1', '5400.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6873, -1, 2011, -1, 5483, -1, 6542, -1], 'generators': [39916800, 43545600, 1680], 'label': '21600.y.1800.e1.a1', 'mobius_quo': None, 'mobius_sub': -240, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '1800.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947664
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': ['3600.a1.a1', '3600.o1.a1', '3600.s1.a1', '3600.i1.b1', '3600.k1.b1', '3600.q1.b1', '3600.i1.a1', '3600.k1.a1', '3600.q1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['30.g1.a1', '30.g1.b1', '36.d1.a1', '36.d1.b1', '60.l1.a1', '60.l1.b1', '360.y1.a1', '360.y1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1786, 1431, 7856, 773, 5617, 1309, 2651, 722], 'generators': [305674, 1960179993], 'label': '21600.y.6.a1.a1', 'mobius_quo': 1, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['360.a1.a1', '360.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.a'}
  • id: 63947665
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.a1.b1'], 'contains': ['100.a1.a1', '100.c1.a1', '100.d1.b1', '150.a1.b1', '150.b1.b1', '150.c1.b1', '200.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3307, -1, 6088, -1, 5751, -1, 5567, -1], 'generators': [39916800, 43545600, 2424, 1680, 5792221743, 5392806153, 83463240], 'label': '21600.y.50.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '50.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1.b1', 'subgroup_fusion': None, 'weyl_group': '432.749'}
  • id: 63947666
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.e1.b1', '360.f1.b1', '600.c1.b1', '600.d1.b1', '900.g1.b1', '900.h1.a1', '900.i1.b1'], 'contains': ['3600.a1.a1', '3600.d1.b1', '3600.i1.a1', '5400.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6873, -1, 2316, -1, 5483, -1, 6565, -1], 'generators': [39916800, 5356806064, 43545600], 'label': '21600.y.1800.e1.b1', 'mobius_quo': None, 'mobius_sub': -240, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '1800.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947667
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.g1.a1', '360.g1.b1', '360.h1.a1', '360.h1.b1', '600.e1.a1', '600.e1.b1', '600.f1.a1', '900.g1.a1', '900.g1.b1', '900.h1.a1', '900.j1.a1', '900.j1.a2'], 'contains': ['3600.a1.a1', '3600.l1.a1', '3600.o1.a1', '5400.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [7472, -1, 3777, -1, 6862, -1, 6629, -1], 'generators': [39916800, 5316890944, 43545600], 'label': '21600.y.1800.f1.a1', 'mobius_quo': None, 'mobius_sub': -32, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947668
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.f1.a1', '600.g1.a1', '900.b1.a1', '900.l1.a1', '900.u1.a1'], 'contains': ['3600.e1.a1', '3600.h1.b1', '5400.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2175, -1, 2650, -1, 5932, -1, 7939, -1], 'generators': [39919224, 1680, 5831851137], 'label': '21600.y.1800.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947669
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.f1.b1', '600.g1.b1', '900.b1.b1', '900.l1.b1', '900.u1.b1'], 'contains': ['3600.e1.b1', '3600.h1.a1', '5400.d1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2175, -1, 7716, -1, 5932, -1, 8424, -1], 'generators': [5313260464, 5832179105, 240], 'label': '21600.y.1800.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947670
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.j1.a1', '360.q1.a1', '600.h1.a1', '600.k1.a1', '900.h1.a1', '900.k1.a1', '900.k1.a2', '900.m1.a1', '900.n1.a1', '900.r1.a1'], 'contains': ['3600.d1.a1', '3600.i1.a1', '3600.o1.a1', '5400.c1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [5933, -1, 3150, -1, 6673, -1, 6783, -1], 'generators': [43545600, 1680, 5316889264], 'label': '21600.y.1800.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947671
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.j1.b1', '360.q1.b1', '600.h1.b1', '600.k1.b1', '900.h1.a1', '900.k1.b1', '900.k1.b2', '900.m1.b1', '900.n1.b1', '900.r1.b1'], 'contains': ['3600.d1.b1', '3600.i1.b1', '3600.o1.a1', '5400.c1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [5933, -1, 3336, -1, 6673, -1, 6806, -1], 'generators': [5356806064, 43545600, 39918480], 'label': '21600.y.1800.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947672
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.r1.a1', '600.h1.a1', '600.m1.a1', '900.e1.a1', '900.l1.a1', '900.s1.a1'], 'contains': ['3600.e1.a1', '3600.j1.a1', '3600.p1.b1', '5400.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [6013, -1, 2413, -1, 5735, -1, 7791, -1], 'generators': [5312973993, 5832138543, 1680], 'label': '21600.y.1800.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947673
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.r1.b1', '600.h1.b1', '600.m1.b1', '900.e1.b1', '900.l1.b1', '900.s1.b1'], 'contains': ['3600.e1.b1', '3600.j1.b1', '3600.p1.a1', '5400.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [6013, -1, 6047, -1, 5735, -1, 8141, -1], 'generators': [4834218540, 4834228620, 4837852404], 'label': '21600.y.1800.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947674
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.s1.a1', '600.h1.a1', '600.l1.a1', '900.t1.a1'], 'contains': ['3600.f1.a1', '3600.k1.a1', '3600.q1.a1', '5400.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [5450, -1, 5796, -1, 5609, -1, 5650, -1], 'generators': [5832138543, 5356519593, 1680], 'label': '21600.y.1800.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.t1.a1', 'old_label': '1800.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947675
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.s1.b1', '600.h1.b1', '600.l1.b1', '900.t1.b1'], 'contains': ['3600.f1.b1', '3600.k1.b1', '3600.q1.b1', '5400.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [5450, -1, 7791, -1, 5609, -1, 6281, -1], 'generators': [4834218540, 4877774220, 4837852404], 'label': '21600.y.1800.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.t1.b1', 'old_label': '1800.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947676
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '10.b1.b1', '25.a1.a1'], 'contains': ['150.e1.a1', '150.e1.b1', '150.f1.a1', '150.f1.a2', '150.g1.a1', '150.g1.b1', '150.h1.a1', '150.i1.a1', '150.i1.a2', '200.d1.a1', '200.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [878, -1, 8907, -1, 7516, -1, 5825, -1], 'generators': [5356806064, 5871767337, 43545600, 2424, 5792262305, 79834440, 1680], 'label': '21600.y.50.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1029'}
  • id: 63947677
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.i1.a1', '600.g1.a1', '900.i1.a1', '900.m1.a1', '900.n1.b1'], 'contains': ['3600.d1.a1', '3600.i1.b1', '5400.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3307, -1, 2612, -1, 6303, -1, 6694, -1], 'generators': [43545600, 2424, 39918480], 'label': '21600.y.1800.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '1800.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947678
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.i1.b1', '600.g1.b1', '900.i1.b1', '900.m1.b1', '900.n1.a1'], 'contains': ['3600.d1.b1', '3600.i1.a1', '5400.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3307, -1, 6356, -1, 6303, -1, 6828, -1], 'generators': [5872095665, 43545600, 5316889264], 'label': '21600.y.1800.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '1800.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947679
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.k1.a1', '600.i1.a1', '900.g1.a1', '900.k1.a1', '900.k1.a2', '900.m1.a1', '900.p1.a1', '900.v1.b1'], 'contains': ['3600.d1.a1', '3600.l1.a1', '5400.e1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2066, -1, 5220, -1, 7695, -1, 7061, -1], 'generators': [5356808488, 43545600, 1680], 'label': '21600.y.1800.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947680
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.k1.b1', '600.i1.b1', '900.g1.b1', '900.k1.b1', '900.k1.b2', '900.m1.b1', '900.p1.a1', '900.v1.a1'], 'contains': ['3600.d1.b1', '3600.l1.a1', '5400.e1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2066, -1, 6251, -1, 7695, -1, 7127, -1], 'generators': [5356806064, 43545600, 5872097345], 'label': '21600.y.1800.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947681
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.i1.a1', '900.a1.a1', '900.l1.a1', '900.y1.b1'], 'contains': ['3600.e1.a1', '3600.m1.b1', '5400.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2229, -1, 4451, -1, 6440, -1, 7906, -1], 'generators': [5312973993, 1680, 5792224167], 'label': '21600.y.1800.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '1800.m1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947682
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.i1.b1', '900.a1.b1', '900.l1.b1', '900.y1.a1'], 'contains': ['3600.e1.b1', '3600.m1.a1', '5400.e1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2229, -1, 8843, -1, 6440, -1, 8391, -1], 'generators': [5313225206, 4834218540, 4834228620], 'label': '21600.y.1800.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '1800.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947683
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.a1', '600.j1.a1', '900.g1.a1', '900.k1.a1', '900.k1.a2', '900.n1.b1', '900.o1.a1', '900.r1.a1'], 'contains': ['3600.d1.a1', '3600.o1.a1', '5400.f1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2712, -1, 3729, -1, 7407, -1, 6983, -1], 'generators': [5316891688, 43545600, 1680], 'label': '21600.y.1800.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.n1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947684
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.l1.b1', '600.j1.b1', '900.g1.b1', '900.k1.b1', '900.k1.b2', '900.n1.a1', '900.o1.a1', '900.r1.b1'], 'contains': ['3600.d1.b1', '3600.o1.a1', '5400.f1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2712, -1, 6176, -1, 7407, -1, 7094, -1], 'generators': [5356806064, 5875726145, 43545600], 'label': '21600.y.1800.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.n1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947685
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.j1.a1', '900.a1.a1', '900.s1.a1', '900.u1.a1'], 'contains': ['3600.e1.a1', '3600.p1.b1', '5400.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2990, -1, 3189, -1, 6396, -1, 7884, -1], 'generators': [5312973993, 5875686567, 1680], 'label': '21600.y.1800.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.o1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947686
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.j1.b1', '900.a1.b1', '900.s1.b1', '900.u1.b1'], 'contains': ['3600.e1.b1', '3600.p1.a1', '5400.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2990, -1, 8502, -1, 6396, -1, 8368, -1], 'generators': [4834218540, 4834228620, 5396687606], 'label': '21600.y.1800.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.o1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947687
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.b1', 'complements': ['360.y1.a1', '360.y1.b1', '360.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.c1.b1'], 'contains': ['120.a1.a1', '180.c1.a1', '300.e1.a1', '360.f1.a1', '600.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5803, 8569, 3721, 9227, 3776, 7782, 4007, 8671], 'generators': [39916800, 43545600, 83473224, 6600], 'label': '21600.y.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['120.a1.a1', '3600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': '60.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947688
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.j1.a1', '900.t1.a1'], 'contains': ['3600.f1.a1', '3600.q1.a1', '5400.f1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [3089, -1, 6692, -1, 6585, -1, 5673, -1], 'generators': [5356519593, 5875686567, 1680], 'label': '21600.y.1800.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.t1.a1', 'old_label': '1800.p1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947689
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.j1.b1', '900.t1.b1'], 'contains': ['3600.f1.b1', '3600.q1.b1', '5400.f1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [3089, -1, 8659, -1, 6585, -1, 6316, -1], 'generators': [4834218540, 4877774220, 5396687606], 'label': '21600.y.1800.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.t1.b1', 'old_label': '1800.p1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.p1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947690
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.t1.a1', '360.t1.b1', '600.u1.a1', '600.u1.b1', '900.h1.a1', '900.n1.a1', '900.n1.b1', '900.o1.a1', '900.p1.a1', '900.v1.a1', '900.v1.b1'], 'contains': ['3600.d1.a1', '3600.d1.b1', '3600.l1.a1', '5400.g1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [1579, -1, 5897, -1, 7613, -1, 6904, -1], 'generators': [5356806064, 43545600, 1680], 'label': '21600.y.1800.q1.a1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.q1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947691
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.a1', '360.m1.a1', '600.k1.a1', '600.l1.a1', '600.m1.a1', '900.e1.b1', '900.u1.b1'], 'contains': ['3600.g1.a1', '3600.h1.a1', '3600.p1.a1', '5400.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [5775, -1, 7120, -1, 5146, -1, 8018, -1], 'generators': [4837857420, 4837847340, 4837852404], 'label': '21600.y.1800.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.r1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947692
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.o1.b1', '360.m1.b1', '600.k1.b1', '600.l1.b1', '600.m1.b1', '900.e1.a1', '900.u1.a1'], 'contains': ['3600.g1.b1', '3600.h1.b1', '3600.p1.b1', '5400.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [5775, -1, 2993, -1, 5146, -1, 7392, -1], 'generators': [5352890793, 39918480, 5792221743], 'label': '21600.y.1800.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.r1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.r1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947693
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '30.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.a1', '600.n1.a1', '600.o1.a1', '600.p1.a1', '900.i1.a1', '900.r1.a1', '900.v1.b1'], 'contains': ['3600.d1.a1', '5400.h1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3232, -1, 6105, -1, 7344, -1, 6727, -1], 'generators': [43545600, 2424, 1680], 'label': '21600.y.1800.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '1800.s1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.s1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947694
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '30.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.b1', '600.n1.b1', '600.o1.b1', '600.p1.b1', '900.i1.b1', '900.r1.b1', '900.v1.a1'], 'contains': ['3600.d1.b1', '5400.h1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3232, -1, 8034, -1, 7344, -1, 6861, -1], 'generators': [5356806064, 5872095665, 43545600], 'label': '21600.y.1800.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '1800.s1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.s1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947695
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.i1.b1', '600.n1.a1', '600.q1.a1', '600.s1.a1', '900.b1.a1', '900.s1.a1', '900.y1.b1'], 'contains': ['3600.e1.a1', '5400.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1421, -1, 6148, -1, 6968, -1, 8050, -1], 'generators': [5791934337, 2424, 1680], 'label': '21600.y.1800.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.b1', 'old_label': '1800.t1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947696
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.i1.a1', '600.n1.b1', '600.q1.b1', '600.s1.b1', '900.b1.b1', '900.s1.b1', '900.y1.a1'], 'contains': ['3600.e1.b1', '5400.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [1421, -1, 9336, -1, 6968, -1, 8467, -1], 'generators': [5313260464, 240, 5792262305], 'label': '21600.y.1800.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.a1.a1', 'old_label': '1800.t1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.t1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947697
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.o1.a1', '600.o1.a1', '600.r1.a1', '600.s1.a1', '900.c1.a1', '900.q1.a1', '900.w1.b1'], 'contains': ['5400.h1.a1', '7200.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4328, -1, 8174, -1, 5779, -1, 7995, -1], 'generators': [840, 2424, 1680], 'label': '21600.y.1800.u1.a1', 'mobius_quo': None, 'mobius_sub': 180, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '1800.u1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947698
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': ['360.y1.a1', '360.y1.b1', '360.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.a1.b1', '30.c1.a1'], 'contains': ['120.a1.b1', '180.c1.b1', '300.e1.b1', '360.f1.b1', '600.d1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5803, 8569, 4327, 5944, 3776, 7782, 2100, 5601], 'generators': [39916800, 43545600, 5795602711, 5396682542], 'label': '21600.y.60.a1.b1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['120.a1.b1', '3600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': '60.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '60.a1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947699
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.b1', '360.o1.b1', '600.o1.b1', '600.r1.b1', '600.s1.b1', '900.c1.b1', '900.q1.b1', '900.w1.a1'], 'contains': ['5400.h1.b1', '7200.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4328, -1, 6066, -1, 5779, -1, 7291, -1], 'generators': [5313260464, 5791933593, 5792262065], 'label': '21600.y.1800.u1.b1', 'mobius_quo': None, 'mobius_sub': 180, 'normal_closure': '360.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '1800.u1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.u1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947700
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.j1.a1', '600.n1.a1', '600.r1.a1', '600.t1.a1', '900.t1.a1'], 'contains': ['3600.f1.a1', '5400.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1331, -1, 7847, -1, 7778, -1, 5706, -1], 'generators': [5835479937, 2424, 1680], 'label': '21600.y.1800.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.c1.a1', 'old_label': '1800.v1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.v1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947701
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.j1.b1', '600.n1.b1', '600.r1.b1', '600.t1.b1', '900.t1.b1'], 'contains': ['3600.f1.b1', '5400.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1331, -1, 9535, -1, 7778, -1, 6418, -1], 'generators': [79833840, 5872095905, 5313260464], 'label': '21600.y.1800.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.c1.b1', 'old_label': '1800.v1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.v1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947702
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.p1.a1', '600.o1.a1', '600.q1.a1', '600.t1.a1', '900.x1.b1'], 'contains': ['5400.h1.a1', '7200.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [623, -1, 8796, -1, 6905, -1, 5836, -1], 'generators': [2424, 79834440, 1680], 'label': '21600.y.1800.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '1800.w1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947703
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.p1.b1', '600.o1.b1', '600.q1.b1', '600.t1.b1', '900.x1.a1'], 'contains': ['5400.h1.b1', '7200.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [623, -1, 8621, -1, 6905, -1, 4643, -1], 'generators': [5313260464, 5871767193, 5792262065], 'label': '21600.y.1800.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.b1', 'old_label': '1800.w1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.w1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947704
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.k1.a1', '450.k1.a2', '600.p1.a1', '600.s1.a1', '600.t1.a1', '900.d1.a1'], 'contains': ['5400.h1.a1', '7200.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1179, -1, 8814, -1, 9236, -1, 8636, -1], 'generators': [2424, 5791933737, 1680], 'label': '21600.y.1800.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '1800.x1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947705
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.k1.a1', '450.k1.a2', '600.p1.b1', '600.s1.b1', '600.t1.b1', '900.d1.b1'], 'contains': ['5400.h1.b1', '7200.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1179, -1, 9825, -1, 9236, -1, 8614, -1], 'generators': [5313260464, 5791933737, 5792262065], 'label': '21600.y.1800.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.b1', 'old_label': '1800.x1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.x1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947706
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.l1.a1', '450.l1.a2', '600.p1.a1', '600.q1.a1', '600.r1.a1', '600.t1.a1'], 'contains': ['5400.h1.a1', '7200.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [236, -1, 9290, -1, 8417, -1, 8346, -1], 'generators': [5871767337, 2424, 1680], 'label': '21600.y.1800.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.d1.a1', 'old_label': '1800.y1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947707
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.l1.a1', '450.l1.a2', '600.p1.b1', '600.q1.b1', '600.r1.b1', '600.t1.b1'], 'contains': ['5400.h1.b1', '7200.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [236, -1, 9961, -1, 8417, -1, 8323, -1], 'generators': [5871767337, 5313260464, 5792262065], 'label': '21600.y.1800.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.d1.b1', 'old_label': '1800.y1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.y1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947708
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.p1.a1', '360.u1.b1', '600.u1.a1', '600.v1.a1', '900.e1.a1', '900.u1.a1', '900.y1.b1'], 'contains': ['3600.e1.a1', '3600.g1.b1', '3600.m1.b1', '5400.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [1952, -1, 4990, -1, 5845, -1, 7415, -1], 'generators': [5312973993, 1680, 5792221743], 'label': '21600.y.1800.z1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '1800.z1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947709
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '20.a1.a1', '30.a1.b1'], 'contains': ['120.j1.a1', '180.c1.a1', '300.a1.a1', '360.c1.a1', '600.a1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5169, -1, 5130, -1, 4878, -1, 4371, -1], 'generators': [5312938592, 5396394392, 83473224, 83462400], 'label': '21600.y.60.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '60.b1.a1', 'projective_image': '21600.y', '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': '120.35'}
  • id: 63947727
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.a1', '450.k1.a2', '600.z1.a1', '900.f1.a1'], 'contains': ['5400.l1.a1', '7200.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4582, -1, 9736, -1, 9777, -1, 8591, -1], 'generators': [5792262809, 5791933737, 5313262144], 'label': '21600.y.1800.bg1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a1', 'old_label': '1800.bg1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947710
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.p1.b1', '360.u1.a1', '600.u1.b1', '600.v1.a1', '900.e1.b1', '900.u1.b1', '900.y1.a1'], 'contains': ['3600.e1.b1', '3600.g1.a1', '3600.m1.a1', '5400.g1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [1952, -1, 8727, -1, 5845, -1, 8176, -1], 'generators': [4834218540, 4834223604, 4834228620], 'label': '21600.y.1800.z1.b1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '1800.z1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.z1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947711
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.w1.a1', '900.a1.b1', '900.l1.b1', '900.u1.b1'], 'contains': ['3600.h1.a1', '3600.m1.a1', '3600.p1.a1', '5400.i1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2656, -1, 7419, -1, 6259, -1, 8241, -1], 'generators': [4917691020, 5396687606, 4917680940], 'label': '21600.y.1800.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.ba1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947712
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.w1.a2', '900.a1.b1', '900.l1.b1', '900.u1.b1'], 'contains': ['3600.h1.a1', '3600.m1.a1', '3600.p1.a1', '5400.i1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2656, -1, 6566, -1, 6259, -1, 8264, -1], 'generators': [5313225206, 4837857420, 4837847340], 'label': '21600.y.1800.ba1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.ba1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ba1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947713
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.w1.b1', '900.a1.a1', '900.l1.a1', '900.u1.a1'], 'contains': ['3600.h1.b1', '3600.m1.b1', '3600.p1.b1', '5400.i1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2656, -1, 2499, -1, 6259, -1, 7814, -1], 'generators': [5396436393, 83464080, 5875686567], 'label': '21600.y.1800.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.ba1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947714
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.w1.b2', '900.a1.a1', '900.l1.a1', '900.u1.a1'], 'contains': ['3600.h1.b1', '3600.m1.b1', '3600.p1.b1', '5400.i1.b2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [2656, -1, 2517, -1, 6259, -1, 7837, -1], 'generators': [5352890793, 39918480, 5792224167], 'label': '21600.y.1800.ba1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.ba1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.ba1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947715
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.a1', '600.w1.a1', '900.g1.b1', '900.k1.a2', '900.m1.b1', '900.n1.a1', '900.z1.a1', '900.z1.a2'], 'contains': ['3600.i1.a1', '3600.l1.a1', '3600.o1.a1', '5400.i1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2498, -1, 3692, -1, 7451, -1, 7006, -1], 'generators': [5875726145, 43545600, 5316889264], 'label': '21600.y.1800.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.bb1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947716
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.a2', '600.w1.a2', '900.g1.b1', '900.k1.a1', '900.m1.b1', '900.n1.a1', '900.z1.a1', '900.z1.a2'], 'contains': ['3600.i1.a1', '3600.l1.a1', '3600.o1.a1', '5400.i1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2498, -1, 3900, -1, 7451, -1, 7028, -1], 'generators': [43545600, 5316889264, 5872097345], 'label': '21600.y.1800.bb1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.bb1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bb1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947717
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.b1', '600.w1.b1', '900.g1.a1', '900.k1.b1', '900.m1.a1', '900.n1.b1', '900.z1.a1', '900.z1.a2'], 'contains': ['3600.i1.b1', '3600.l1.a1', '3600.o1.a1', '5400.i1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2498, -1, 3074, -1, 7451, -1, 6937, -1], 'generators': [5316891688, 43545600, 39918480], 'label': '21600.y.1800.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.bb1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947718
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.v1.b2', '600.w1.b2', '900.g1.a1', '900.k1.b2', '900.m1.a1', '900.n1.b1', '900.z1.a1', '900.z1.a2'], 'contains': ['3600.i1.b1', '3600.l1.a1', '3600.o1.a1', '5400.i1.b2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2498, -1, 3092, -1, 7451, -1, 6960, -1], 'generators': [5356808488, 43545600, 39918480], 'label': '21600.y.1800.bb1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.bb1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bb1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947719
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.w1.b1', '600.x1.a1', '600.y1.a1', '900.e1.b1', '900.l1.b1'], 'contains': ['3600.h1.a1', '3600.j1.b1', '3600.m1.a1', '5400.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [6970, -1, 5742, -1, 4997, -1, 8095, -1], 'generators': [4834223604, 4837857420, 4837847340], 'label': '21600.y.1800.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '1800.bc1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947720
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '20.a1.b1', '30.a1.a1'], 'contains': ['120.j1.b1', '180.c1.b1', '300.a1.b1', '360.c1.b1', '600.a1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 30, 'diagramx': [5169, -1, 5985, -1, 4878, -1, 2604, -1], 'generators': [5791974151, 83462640, 5313220382, 83462400], 'label': '21600.y.60.b1.b1', '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.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947721
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.w1.a1', '600.x1.a1', '600.y1.b1', '900.e1.a1', '900.l1.a1'], 'contains': ['3600.h1.b1', '3600.j1.a1', '3600.m1.b1', '5400.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [6970, -1, 1983, -1, 4997, -1, 7697, -1], 'generators': [5352890793, 5832138543, 39918480], 'label': '21600.y.1800.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '1800.bc1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947722
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.x1.a1', '360.x1.b1', '600.y1.a1', '600.y1.b1', '900.h1.a1', '900.m1.a1', '900.m1.b1', '900.z1.a1', '900.z1.a2'], 'contains': ['3600.i1.a1', '3600.i1.b1', '3600.l1.a1', '5400.j1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [7007, -1, 2393, -1, 6629, -1, 6760, -1], 'generators': [43545600, 39918480, 5316889264], 'label': '21600.y.1800.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.bd1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947723
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.j1.a1', '900.k1.a1', '900.k1.a2', '900.k1.b1', '900.k1.b2', '900.o1.a1', '900.z1.a2'], 'contains': ['3600.l1.a1', '3600.o1.a1', '5400.k1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [889, -1, 5409, -1, 7891, -1, 7203, -1], 'generators': [5316891688, 43545600, 5872097345], 'label': '21600.y.1800.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.be1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947724
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.j1.a2', '900.k1.a1', '900.k1.a2', '900.k1.b1', '900.k1.b2', '900.o1.a1', '900.z1.a1'], 'contains': ['3600.l1.a1', '3600.o1.a1', '5400.k1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [889, -1, 5362, -1, 7891, -1, 7225, -1], 'generators': [5316890008, 43545600, 5872097345], 'label': '21600.y.1800.be1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '1800.be1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.be1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947725
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.z1.a1', '900.j1.a1', '900.p1.a1', '900.z1.a1'], 'contains': ['3600.l1.a1', '5400.l1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [795, -1, 7363, -1, 8985, -1, 7170, -1], 'generators': [5356808488, 43545600, 5872097345], 'label': '21600.y.1800.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a2', 'old_label': '1800.bf1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947726
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.z1.a2', '900.j1.a2', '900.p1.a1', '900.z1.a2'], 'contains': ['3600.l1.a1', '5400.l1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [795, -1, 7318, -1, 8985, -1, 7258, -1], 'generators': [5356806808, 43545600, 5872097345], 'label': '21600.y.1800.bf1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '1800.bf1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bf1.a2', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 63947728
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.b1', '450.k1.a1', '600.z1.a2', '900.f1.a2'], 'contains': ['5400.l1.a2', '7200.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4582, -1, 9499, -1, 9777, -1, 8568, -1], 'generators': [5792264489, 5313262144, 5791935177], 'label': '21600.y.1800.bg1.a2', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.h1.a2', 'old_label': '1800.bg1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bg1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947729
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.l1.a1', '600.z1.a2'], 'contains': ['5400.l1.a2', '7200.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [1896, -1, 9802, -1, 9890, -1, 8500, -1], 'generators': [5835480777, 5792264489, 5313262144], 'label': '21600.y.1800.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.z1.a2', 'old_label': '1800.bh1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947730
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '1800.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.l1.a2', '600.z1.a1'], 'contains': ['5400.l1.a1', '7200.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [1896, -1, 9883, -1, 9890, -1, 8523, -1], 'generators': [5871767337, 5792262809, 5313262144], 'label': '21600.y.1800.bh1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.z1.a1', 'old_label': '1800.bh1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.bh1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63947731
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '30.b1.a1'], 'contains': ['120.f1.a1', '180.a1.a1', '180.f1.a1', '240.a1.a1', '300.e1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5713, -1, 3555, -1, 4211, -1, 1972, -1], 'generators': [39916800, 43545600, 2424, 1680, 5875684380, 83463240], 'label': '21600.y.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.c1.a1', 'projective_image': '21600.y', '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': '144.190'}
  • id: 63947732
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.a1.a1', '720.b1.a1', '1080.a1.a1', '1080.b1.b1', '1080.c1.a1'], 'contains': ['4320.a1.a1', '10800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7966, -1, 1103, -1, 1901, -1, 2016, -1], 'generators': [39916800, 5792221740], 'label': '21600.y.2160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '2160.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947733
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.a1.b1', '720.b1.b1', '1080.a1.b1', '1080.b1.a1', '1080.c1.b1'], 'contains': ['4320.a1.b1', '10800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7966, -1, 641, -1, 1901, -1, 4057, -1], 'generators': [83468400, 83462400], 'label': '21600.y.2160.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '2160.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947734
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.c1.a1', '1080.d1.a1'], 'contains': ['4320.b1.a1', '10800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [9534, -1, 706, -1, 3198, -1, 2515, -1], 'generators': [39916800, 4833942753], 'label': '21600.y.2160.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1.a1', 'old_label': '2160.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947735
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '720.c1.b1', '1080.d1.b1'], 'contains': ['4320.b1.b1', '10800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [9534, -1, 664, -1, 3198, -1, 2669, -1], 'generators': [39916800, 5832191222], 'label': '21600.y.2160.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.b1.a1', 'old_label': '2160.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947736
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '720.d1.a1', '720.e1.a1', '1080.a1.a1', '1080.e1.a1', '1080.f1.a1', '1080.g1.a1', '1080.h1.a1', '1080.i1.a1', '1080.k1.a1'], 'contains': ['4320.a1.a1', '10800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5344, -1, 3502, -1, 3251, -1, 2163, -1], 'generators': [1680, 5792223420], 'label': '21600.y.2160.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '2160.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947737
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.b1', '720.d1.b1', '720.e1.b1', '1080.a1.b1', '1080.e1.b1', '1080.f1.b1', '1080.g1.b1', '1080.h1.b1', '1080.i1.b1', '1080.k1.b1'], 'contains': ['4320.a1.b1', '10800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5344, -1, 5536, -1, 3251, -1, 4204, -1], 'generators': [6000, 4834218540], 'label': '21600.y.2160.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '2160.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947738
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '432.b1.a1', '720.f1.a1', '720.g1.a1', '720.h1.a1', '1080.b1.a1', '1080.j1.a1', '1080.k1.b1'], 'contains': ['4320.a1.b1', '10800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5243, -1, 3393, -1, 2637, -1, 4009, -1], 'generators': [6000, 17520], 'label': '21600.y.2160.d1.a1', 'mobius_quo': None, 'mobius_sub': 180, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '2160.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947739
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.b1', '432.b1.b1', '720.f1.b1', '720.g1.b1', '720.h1.b1', '1080.b1.b1', '1080.j1.b1', '1080.k1.a1'], 'contains': ['4320.a1.a1', '10800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5243, -1, 5566, -1, 2637, -1, 1968, -1], 'generators': [4834258861, 5792221740], 'label': '21600.y.2160.d1.b1', 'mobius_quo': None, 'mobius_sub': 180, 'normal_closure': '360.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '2160.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947740
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.i1.a1', '720.j1.a1', '720.k1.a1', '1080.a1.b1', '1080.e1.b1', '1080.j1.a1', '1080.l1.a1', '1080.l1.a2', '1080.m1.a1'], 'contains': ['4320.a1.b1', '10800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7645, -1, 1191, -1, 2048, -1, 4085, -1], 'generators': [6000, 4837847340], 'label': '21600.y.2160.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '2160.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947741
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '540.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.b1', '720.i1.b1', '720.j1.b1', '720.k1.b1', '1080.a1.a1', '1080.e1.a1', '1080.j1.b1', '1080.l1.b1', '1080.l1.b2', '1080.m1.b1'], 'contains': ['4320.a1.a1', '10800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7645, -1, 1484, -1, 2048, -1, 2044, -1], 'generators': [39918480, 5832140220], 'label': '21600.y.2160.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '2160.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947742
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '30.b1.b1'], 'contains': ['120.f1.b1', '180.a1.b1', '180.f1.b1', '240.a1.b1', '300.e1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5713, -1, 7460, -1, 4211, -1, 3751, -1], 'generators': [4877764140, 39916800, 43545600, 1963791510, 2043383282, 1959914882], 'label': '21600.y.60.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '60.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.b1', 'subgroup_fusion': None, 'weyl_group': '144.190'}
  • id: 63947743
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '720.l1.a1', '720.m1.a1', '1080.b1.b1', '1080.f1.a1', '1080.m1.b1'], 'contains': ['4320.a1.a1', '10800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8160, -1, 1324, -1, 1596, -1, 1991, -1], 'generators': [4917721261, 5792221740], 'label': '21600.y.2160.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '2160.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.f1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947744
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.b1', '720.l1.b1', '720.m1.b1', '1080.b1.a1', '1080.f1.b1', '1080.m1.a1'], 'contains': ['4320.a1.b1', '10800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8160, -1, 830, -1, 1596, -1, 4032, -1], 'generators': [6000, 39934320], 'label': '21600.y.2160.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '2160.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.f1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947745
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.d1.a1', '720.n1.a1', '720.p1.a1', '1080.c1.a1', '1080.g1.a1', '1080.k1.a1', '1080.l1.b1', '1080.l1.b2', '1080.m1.b1'], 'contains': ['4320.a1.a1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8217, -1, 4852, -1, 2745, -1, 2092, -1], 'generators': [4834260541, 5792221740], 'label': '21600.y.2160.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.a1', 'old_label': '2160.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.g1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947746
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.d1.a1', '720.n1.b1', '720.p1.b1', '1080.c1.b1', '1080.g1.b1', '1080.k1.b1', '1080.l1.a1', '1080.l1.a2', '1080.m1.a1'], 'contains': ['4320.a1.b1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8217, -1, 4598, -1, 2745, -1, 4133, -1], 'generators': [6000, 5313237662], 'label': '21600.y.2160.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.c1.b1', 'old_label': '2160.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.g1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947747
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.a1', '432.d1.a1', '720.o1.a1', '1080.d1.a1'], 'contains': ['4320.b1.a1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9623, -1, 4945, -1, 3974, -1, 2540, -1], 'generators': [4834240284, 4833942753], 'label': '21600.y.2160.h1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.a1', 'old_label': '2160.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.h1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947748
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.b1', '432.d1.a1', '720.o1.b1', '1080.d1.b1'], 'contains': ['4320.b1.b1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9623, -1, 4877, -1, 3974, -1, 2695, -1], 'generators': [4834240284, 5792274422], 'label': '21600.y.2160.h1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.h1.b1', 'old_label': '2160.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.h1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947749
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.e1.a1', '720.q1.a1', '720.s1.a1', '720.t1.b1', '1080.c1.a1', '1080.f1.a1', '1080.h1.a1', '1080.j1.b1', '1080.l1.b1', '1080.l1.b2'], 'contains': ['4320.a1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7863, -1, 2171, -1, 2494, -1, 2069, -1], 'generators': [4917722941, 5792221740], 'label': '21600.y.2160.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.a1', 'old_label': '2160.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.i1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947750
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.e1.a1', '720.q1.b1', '720.s1.b1', '720.t1.a1', '1080.c1.b1', '1080.f1.b1', '1080.h1.b1', '1080.j1.a1', '1080.l1.a1', '1080.l1.a2'], 'contains': ['4320.a1.b1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 270, 'diagramx': [7863, -1, 1589, -1, 2494, -1, 4110, -1], 'generators': [6000, 5396700062], 'label': '21600.y.2160.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '270.a1.b1', 'old_label': '2160.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.i1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947751
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.e1.a1', '720.r1.a1', '1080.d1.a1'], 'contains': ['4320.b1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [9711, -1, 1968, -1, 3915, -1, 2489, -1], 'generators': [4837869084, 4833942753], 'label': '21600.y.2160.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.d1.a1', 'old_label': '2160.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.j1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947752
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2160.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.e1.a1', '720.r1.b1', '1080.d1.b1'], 'contains': ['4320.b1.b1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [9711, -1, 1851, -1, 3915, -1, 2643, -1], 'generators': [5792274422, 4837869084], 'label': '21600.y.2160.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.d1.b1', 'old_label': '2160.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.j1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63947753
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.a1.a1'], 'contains': ['120.b1.a1', '120.c1.b1', '120.d1.a1', '120.e1.a1', '120.g1.b1', '120.h1.a1', '120.k1.b1', '180.b1.a1', '180.g1.a1', '300.g1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7191, -1, 4088, -1, 2309, -1, 1784, -1], 'generators': [2043377285, 39916800, 43545600, 5832178862, 4877776404, 4837848924], 'label': '21600.y.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.a1', 'old_label': '60.d1.a1', 'projective_image': '21600.y', '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': '360.137'}
  • id: 63947754
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.a1', '600.o1.a1', '800.a1.a1', '1200.b1.a1', '1200.d1.b1', '1200.e1.a1', '1200.h1.a1', '1200.k1.b1', '1200.l1.a1', '1200.o1.a1'], 'contains': ['7200.a1.a1', '7200.b1.a1', '7200.c1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5666, -1, 7968, -1, 5824, -1, 6050, -1], 'generators': [43545600, 79834440], 'label': '21600.y.2400.a1.a1', 'mobius_quo': None, 'mobius_sub': 120, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '2400.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947755
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.b1', '600.o1.b1', '800.a1.a1', '1200.b1.b1', '1200.d1.a1', '1200.e1.b1', '1200.h1.b1', '1200.k1.a1', '1200.l1.b1', '1200.o1.b1'], 'contains': ['7200.a1.a1', '7200.b1.b1', '7200.c1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5666, -1, 1440, -1, 5824, -1, 5293, -1], 'generators': [43545600, 5871767193], 'label': '21600.y.2400.a1.b1', 'mobius_quo': None, 'mobius_sub': 120, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '2400.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947756
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2400.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.p1.a1', '600.p1.b1', '600.z1.a1', '600.z1.a2', '800.a1.a1', '1200.c1.a1', '1200.m1.a1', '1200.p1.a1'], 'contains': ['7200.a1.a1', '7200.d1.a1', '7200.e1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [4769, -1, 9623, -1, 8314, -1, 6519, -1], 'generators': [5871767337, 43545600], 'label': '21600.y.2400.b1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.b1.a1', 'old_label': '2400.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947757
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.q1.b1', '600.r1.a1', '800.a1.a1', '1200.f1.a1', '1200.i1.a1', '1200.q1.a1'], 'contains': ['7200.b1.a1', '7200.c1.a1', '7200.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [3176, -1, 8331, -1, 6223, -1, 5542, -1], 'generators': [5871767337, 240], 'label': '21600.y.2400.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.c1.a1', 'old_label': '2400.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947758
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.q1.a1', '600.r1.b1', '800.a1.a1', '1200.f1.b1', '1200.i1.b1', '1200.q1.b1'], 'contains': ['7200.b1.b1', '7200.c1.b1', '7200.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [3176, -1, 9552, -1, 6223, -1, 6183, -1], 'generators': [79833840, 5835479337], 'label': '21600.y.2400.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.c1.b1', 'old_label': '2400.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947759
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2400.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.s1.a1', '600.s1.b1', '800.a1.a1', '1200.a1.a1', '1200.g1.a1', '1200.g1.b1', '1200.j1.a1', '1200.j1.b1', '1200.n1.a1', '1200.r1.a1'], 'contains': ['7200.b1.a1', '7200.b1.b1', '7200.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [4588, -1, 8228, -1, 6773, -1, 7513, -1], 'generators': [240, 5791933737], 'label': '21600.y.2400.d1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.a1', 'old_label': '2400.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63947760
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2400.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.t1.a1', '600.t1.b1', '800.a1.a1', '1200.s1.a1'], 'contains': ['7200.c1.a1', '7200.c1.b1', '7200.d1.a1', '7200.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 400, 'diagramx': [4506, -1, 9702, -1, 8109, -1, 5516, -1], 'generators': [79833840, 5871767337], 'label': '21600.y.2400.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '400.e1.a1', 'old_label': '2400.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2400.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947761
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.a1.a1', '900.a1.a1', '900.g1.a1', '1350.a1.a1', '1350.b1.b1'], 'contains': ['5400.a1.a1', '5400.b1.a1', '5400.e1.a1', '5400.f1.a1', '5400.i1.b1', '5400.i1.b2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2765, -1, 4169, -1, 7497, -1, 8865, -1], 'generators': [39916800, 1680, 5313262888], 'label': '21600.y.2700.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947762
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.a1.b1', '900.a1.b1', '900.g1.b1', '1350.a1.a1', '1350.b1.a1'], 'contains': ['5400.a1.b1', '5400.b1.a1', '5400.e1.b1', '5400.f1.b1', '5400.i1.a1', '5400.i1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2765, -1, 6570, -1, 7497, -1, 8994, -1], 'generators': [39916800, 5313260464, 5792263745], 'label': '21600.y.2700.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947763
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.c1.a1', '540.c1.b1', '900.e1.a1', '900.e1.b1', '900.h1.a1', '1350.a1.a1', '1350.b1.a1', '1350.b1.b1'], 'contains': ['5400.a1.a1', '5400.a1.b1', '5400.b1.a1', '5400.c1.a1', '5400.c1.b1', '5400.g1.a1', '5400.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [7096, -1, 4309, -1, 6742, -1, 8687, -1], 'generators': [39916800, 5313260464, 1680], 'label': '21600.y.2700.b1.a1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947764
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.a1.b1'], 'contains': ['120.b1.b1', '120.c1.a1', '120.d1.b1', '120.e1.b1', '120.g1.a1', '120.h1.b1', '120.k1.a1', '180.b1.b1', '180.g1.b1', '300.g1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7191, -1, 2230, -1, 2309, -1, 3225, -1], 'generators': [5160, 39916800, 43545600, 1963814094, 1959937465, 83472720], 'label': '21600.y.60.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.d1.b1', 'old_label': '60.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.b1', 'subgroup_fusion': None, 'weyl_group': '360.137'}
  • id: 63947765
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.b1.a1', '900.b1.a1', '900.c1.a1', '900.d1.a1', '900.i1.a1', '1350.b1.b1'], 'contains': ['5400.a1.a1', '5400.d1.a1', '5400.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3242, -1, 3548, -1, 6349, -1, 8661, -1], 'generators': [39916800, 2424, 1680], 'label': '21600.y.2700.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '2700.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947766
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.b1.b1', '900.b1.b1', '900.c1.b1', '900.d1.b1', '900.i1.b1', '1350.b1.a1'], 'contains': ['5400.a1.b1', '5400.d1.b1', '5400.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3242, -1, 7596, -1, 6349, -1, 8713, -1], 'generators': [39916800, 5313260464, 5792262065], 'label': '21600.y.2700.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '2700.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.c1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947767
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.f1.a1', '900.j1.a1', '1350.a1.a1'], 'contains': ['5400.b1.a1', '5400.k1.a1', '5400.l1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2601, -1, 7004, -1, 8464, -1, 9072, -1], 'generators': [39916800, 5792263745, 5313262888], 'label': '21600.y.2700.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.b1.a2', 'old_label': '2700.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947768
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.f1.a2', '900.j1.a2', '1350.a1.a1'], 'contains': ['5400.b1.a1', '5400.k1.a2', '5400.l1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2601, -1, 7195, -1, 8464, -1, 9046, -1], 'generators': [39916800, 5792263745, 5313261208], 'label': '21600.y.2700.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.b1.a1', 'old_label': '2700.d1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.d1.a2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947769
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.k1.a1', '1350.a1.a1', '1350.c1.a1', '1350.d1.b1'], 'contains': ['5400.c1.a1', '5400.e1.a1', '5400.f1.a1', '5400.i1.a2', '5400.k1.a1', '5400.k1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [845, -1, 6708, -1, 7960, -1, 9253, -1], 'generators': [5316891688, 5795892545, 1680], 'label': '21600.y.2700.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947770
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.k1.a2', '1350.a1.a1', '1350.c1.a1', '1350.d1.b1'], 'contains': ['5400.c1.a1', '5400.e1.a1', '5400.f1.a1', '5400.i1.a1', '5400.k1.a1', '5400.k1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [845, -1, 6729, -1, 7960, -1, 9227, -1], 'generators': [5875726145, 1680, 5313262888], 'label': '21600.y.2700.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.e1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.e1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947771
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.k1.b1', '1350.a1.a1', '1350.c1.a1', '1350.d1.a1'], 'contains': ['5400.c1.b1', '5400.e1.b1', '5400.f1.b1', '5400.i1.b1', '5400.k1.a1', '5400.k1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [845, -1, 6932, -1, 7960, -1, 9124, -1], 'generators': [5316891688, 5795892545, 3630480], 'label': '21600.y.2700.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947772
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.k1.b2', '1350.a1.a1', '1350.c1.a1', '1350.d1.a1'], 'contains': ['5400.c1.b1', '5400.e1.b1', '5400.f1.b1', '5400.i1.b2', '5400.k1.a1', '5400.k1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [845, -1, 7075, -1, 7960, -1, 9175, -1], 'generators': [5875726145, 83464080, 5313262888], 'label': '21600.y.2700.e1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.e1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.e1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947773
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.d1.a1', '900.l1.a1', '900.m1.a1', '1350.b1.b1', '1350.c1.a1'], 'contains': ['5400.c1.a1', '5400.d1.a1', '5400.e1.a1', '5400.i1.b1', '5400.i1.b2', '5400.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2723, -1, 3864, -1, 6815, -1, 8890, -1], 'generators': [2424, 5316889264, 3630480], 'label': '21600.y.2700.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947774
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.d1.b1', '900.l1.b1', '900.m1.b1', '1350.b1.a1', '1350.c1.a1'], 'contains': ['5400.c1.b1', '5400.d1.b1', '5400.e1.b1', '5400.i1.a1', '5400.i1.a2', '5400.j1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2723, -1, 6649, -1, 6815, -1, 8942, -1], 'generators': [5313260464, 5792263745, 39918480], 'label': '21600.y.2700.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947775
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.b1', '12.b1.b1', '12.c1.a1', '18.a1.a1', '30.b1.b1', '30.c1.a1', '36.b1.a1', '60.d1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5991, -1, 4287, -1, 3059, -1, 1661, -1], 'generators': [5160, 39916800, 43545600, 80104015, 5352848792, 83472720], 'label': '21600.y.6.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '6.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3600.de'}
  • id: 63947776
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['120.l1.a1', '180.d1.a1', '300.h1.a1', '360.h1.a1', '600.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8546, -1, 7818, -1, 9388, -1, 2818, -1], 'generators': [39916800, 5392767776, 43545600, 80086591], 'label': '21600.y.60.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.a1', 'old_label': '60.e1.a1', 'projective_image': '21600.y', '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': '360.121'}
  • id: 63947777
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.f1.b1', '900.n1.a1', '900.u1.b1', '1350.b1.a1', '1350.c1.a1', '1350.d1.b1'], 'contains': ['5400.c1.a1', '5400.d1.b1', '5400.f1.b1', '5400.g1.a1', '5400.i1.a1', '5400.i1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2495, -1, 6983, -1, 7547, -1, 8968, -1], 'generators': [5792263745, 1680, 5316889264], 'label': '21600.y.2700.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947778
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.f1.a1', '900.n1.b1', '900.u1.a1', '1350.b1.b1', '1350.c1.a1', '1350.d1.a1'], 'contains': ['5400.c1.b1', '5400.d1.a1', '5400.f1.a1', '5400.g1.a1', '5400.i1.b1', '5400.i1.b2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2495, -1, 4200, -1, 7547, -1, 8839, -1], 'generators': [5313260464, 2424, 39918480], 'label': '21600.y.2700.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947779
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.o1.a1', '1350.a1.a1', '1350.d1.a1', '1350.d1.b1'], 'contains': ['5400.f1.a1', '5400.f1.b1', '5400.g1.a1', '5400.k1.a1', '5400.k1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [889, -1, 7106, -1, 8010, -1, 9098, -1], 'generators': [5316891688, 5792263745, 1680], 'label': '21600.y.2700.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947780
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.p1.a1', '1350.a1.a1', '1350.c1.a1', '1350.e1.a1'], 'contains': ['5400.e1.a1', '5400.e1.b1', '5400.g1.a1', '5400.l1.a1', '5400.l1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [385, -1, 8392, -1, 8221, -1, 9279, -1], 'generators': [5792263745, 1680, 5313262888], 'label': '21600.y.2700.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '2700.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947781
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.e1.a1', '900.q1.a1', '900.r1.a1', '900.s1.a1', '900.t1.a1', '1350.b1.b1', '1350.d1.b1'], 'contains': ['5400.c1.a1', '5400.f1.a1', '5400.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3734, -1, 5939, -1, 7278, -1, 8739, -1], 'generators': [2424, 1680, 5316889264], 'label': '21600.y.2700.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '2700.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.j1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947782
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.e1.b1', '900.q1.b1', '900.r1.b1', '900.s1.b1', '900.t1.b1', '1350.b1.a1', '1350.d1.a1'], 'contains': ['5400.c1.b1', '5400.f1.b1', '5400.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3734, -1, 8234, -1, 7278, -1, 8765, -1], 'generators': [5875726145, 5313260464, 83464080], 'label': '21600.y.2700.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.b1', 'old_label': '2700.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.j1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947783
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.g1.b1', '900.v1.a1', '900.w1.a1', '900.x1.a1', '900.y1.a1', '1350.b1.a1', '1350.d1.a1', '1350.e1.a1'], 'contains': ['5400.e1.b1', '5400.g1.a1', '5400.h1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1055, -1, 8738, -1, 7844, -1, 9020, -1], 'generators': [5313260464, 5792263745, 1680], 'label': '21600.y.2700.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '2700.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.k1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947784
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['540.g1.a1', '900.v1.b1', '900.w1.b1', '900.x1.b1', '900.y1.b1', '1350.b1.b1', '1350.d1.b1', '1350.e1.a1'], 'contains': ['5400.e1.a1', '5400.g1.a1', '5400.h1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1055, -1, 7766, -1, 7844, -1, 8916, -1], 'generators': [5313260464, 2424, 1680], 'label': '21600.y.2700.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '2700.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.k1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947785
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.z1.a1', '1350.a1.a1', '1350.c1.a1'], 'contains': ['5400.i1.a1', '5400.i1.a2', '5400.i1.b1', '5400.i1.b2', '5400.j1.a1', '5400.k1.a2', '5400.l1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [688, -1, 6380, -1, 8115, -1, 9201, -1], 'generators': [5792263745, 39918480, 5313262888], 'label': '21600.y.2700.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947786
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '2700.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.z1.a2', '1350.a1.a1', '1350.c1.a1'], 'contains': ['5400.i1.a1', '5400.i1.a2', '5400.i1.b1', '5400.i1.b2', '5400.j1.a1', '5400.k1.a1', '5400.l1.a2'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [688, -1, 6401, -1, 8115, -1, 9149, -1], 'generators': [5316891688, 5792263745, 3630480], 'label': '21600.y.2700.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '2700.l1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2700.l1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947787
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['120.l1.b1', '180.d1.b1', '300.h1.a2', '360.h1.b1', '600.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8546, -1, 7862, -1, 9388, -1, 2897, -1], 'generators': [39916800, 43545600, 2040079137, 40216474], 'label': '21600.y.60.e1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.e1.b1', 'old_label': '60.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947788
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.a1.a1', 'complements': ['6.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['720.b1.a1', '720.b1.b1', '720.c1.a1', '720.c1.b1', '1200.b1.a1', '1200.b1.b1', '1200.c1.a1', '1800.e1.a1', '1800.e1.b1', '1800.f1.a1'], 'contains': ['7200.a1.a1', '10800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7505, 8387, 1097, 8344, 5576, 9018, 6253, 8671], 'generators': [39916800, 43545600], 'label': '21600.y.3600.a1.a1', 'mobius_quo': 0, 'mobius_sub': 10800, 'normal_closure': '3600.a1.a1', 'normal_contained_in': ['60.a1.a1', '60.a1.b1'], 'normal_contains': ['7200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3600.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3600.a', 'quotient_action_kernel_order': 3600, 'quotient_fusion': None, 'short_label': '3600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947789
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '900.c1.a1', '1200.a1.a1', '1200.b1.a1', '1800.a1.b1', '1800.b1.a1', '1800.c1.a1'], 'contains': ['7200.b1.a1', '10800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6257, -1, 4777, -1, 5439, -1, 7777, -1], 'generators': [83463240, 83462400], 'label': '21600.y.3600.b1.a1', 'mobius_quo': None, 'mobius_sub': 120, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '3600.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947790
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.b1', '900.c1.b1', '1200.a1.a1', '1200.b1.b1', '1800.a1.a1', '1800.b1.b1', '1800.c1.b1'], 'contains': ['7200.b1.b1', '10800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6257, -1, 1886, -1, 5439, -1, 7537, -1], 'generators': [5875395993, 83462400], 'label': '21600.y.3600.b1.b1', 'mobius_quo': None, 'mobius_sub': 120, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '3600.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947791
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.d1.a1', '900.d1.b1', '900.f1.a1', '900.f1.a2', '1200.a1.a1', '1200.c1.a1', '1800.d1.a1'], 'contains': ['7200.d1.a1', '10800.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [4455, -1, 6208, -1, 8201, -1, 8162, -1], 'generators': [5875396137, 83462400], 'label': '21600.y.3600.c1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.b1.a1', 'old_label': '3600.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947792
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '30.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.d1.a1', '720.f1.a1', '1200.d1.a1', '1200.e1.a1', '1800.e1.a1', '1800.h1.a1', '1800.k1.a1', '1800.l1.a1', '1800.n1.a1', '1800.q1.a1', '1800.s1.a1'], 'contains': ['7200.a1.a1', '10800.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4532, -1, 3997, -1, 6457, -1, 6694, -1], 'generators': [43545600, 1680], 'label': '21600.y.3600.d1.a1', 'mobius_quo': None, 'mobius_sub': 240, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '3600.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947793
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '30.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.d1.b1', '720.f1.b1', '1200.d1.b1', '1200.e1.b1', '1800.e1.b1', '1800.h1.b1', '1800.k1.b1', '1800.l1.b1', '1800.n1.b1', '1800.q1.a1', '1800.s1.b1'], 'contains': ['7200.a1.a1', '10800.b1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4532, -1, 6460, -1, 6457, -1, 6783, -1], 'generators': [5356806064, 43545600], 'label': '21600.y.3600.d1.b1', 'mobius_quo': None, 'mobius_sub': 240, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '3600.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947794
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.g1.a1', '900.w1.a1', '1200.d1.a1', '1200.g1.a1', '1800.a1.a1', '1800.g1.a1', '1800.i1.a1', '1800.m1.a1', '1800.o1.a1', '1800.t1.a1', '1800.z1.a1'], 'contains': ['7200.b1.b1', '10800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2101, -1, 3959, -1, 5879, -1, 7697, -1], 'generators': [5791935273, 1680], 'label': '21600.y.3600.e1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '3600.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947795
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.g1.b1', '900.w1.b1', '1200.d1.b1', '1200.g1.b1', '1800.a1.b1', '1800.g1.b1', '1800.i1.b1', '1800.m1.b1', '1800.o1.b1', '1800.t1.b1', '1800.z1.b1'], 'contains': ['7200.b1.a1', '10800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [2101, -1, 8589, -1, 5879, -1, 7868, -1], 'generators': [840, 5313260464], 'label': '21600.y.3600.e1.b1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '3600.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947813
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.y1.a1', '360.y1.b1', '1200.m1.a1', '1200.n1.a1', '1800.d1.a1'], 'contains': ['7200.d1.a1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [6436, -1, 9570, -1, 8268, -1, 7890, -1], 'generators': [15988, 1959931561], 'label': '21600.y.3600.n1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.f1.a1', 'old_label': '3600.n1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947796
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.h1.a1', '900.x1.a1', '1200.d1.a1', '1200.f1.a1', '1800.j1.a1', '1800.p1.a1', '1800.v1.a1'], 'contains': ['7200.c1.a1', '10800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [1864, -1, 7541, -1, 6270, -1, 5618, -1], 'generators': [1680, 5871768873], 'label': '21600.y.3600.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.m1.a1', 'old_label': '3600.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947797
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.h1.b1', '900.x1.b1', '1200.d1.b1', '1200.f1.b1', '1800.j1.b1', '1800.p1.b1', '1800.v1.b1'], 'contains': ['7200.c1.b1', '10800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [1864, -1, 9256, -1, 6270, -1, 6299, -1], 'generators': [5313260464, 79834440], 'label': '21600.y.3600.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.m1.b1', 'old_label': '3600.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947798
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.b1.a1'], 'contains': ['120.f1.a1', '180.i1.a1', '180.j1.a1', '240.e1.a1', '300.j1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6235, -1, 5237, -1, 3970, -1, 1901, -1], 'generators': [5872055580, 43545600, 2424, 79834440, 1680, 4917721261], 'label': '21600.y.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.f1.a1', 'projective_image': '21600.y', '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': '720.797'}
  • id: 63947799
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '720.e1.a1', '1200.e1.a1', '1200.f1.a1', '1200.g1.a1', '1800.b1.a1', '1800.r1.a1', '1800.z1.b1'], 'contains': ['7200.b1.a1', '10800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5124, -1, 7689, -1, 5314, -1, 7719, -1], 'generators': [10080, 5064], 'label': '21600.y.3600.g1.a1', 'mobius_quo': None, 'mobius_sub': 180, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '3600.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947800
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.b1', '720.e1.b1', '1200.e1.b1', '1200.f1.b1', '1200.g1.b1', '1800.b1.b1', '1800.r1.b1', '1800.z1.a1'], 'contains': ['7200.b1.b1', '10800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5124, -1, 5600, -1, 5314, -1, 7353, -1], 'generators': [5312972313, 5792221743], 'label': '21600.y.3600.g1.b1', 'mobius_quo': None, 'mobius_sub': 180, 'normal_closure': '360.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '3600.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947801
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.l1.a1', '900.q1.a1', '1200.h1.a1', '1200.i1.a1', '1200.j1.a1', '1800.a1.b1', '1800.g1.b1', '1800.r1.a1', '1800.ba1.a1', '1800.ba1.a2', '1800.bc1.a1'], 'contains': ['7200.b1.a1', '10800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [4985, -1, 6190, -1, 5162, -1, 7822, -1], 'generators': [840, 5316889264], 'label': '21600.y.3600.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '3600.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947802
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.l1.b1', '900.q1.b1', '1200.h1.b1', '1200.i1.b1', '1200.j1.b1', '1800.a1.a1', '1800.g1.a1', '1800.r1.b1', '1800.ba1.b1', '1800.ba1.b2', '1800.bc1.b1'], 'contains': ['7200.b1.b1', '10800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [4985, -1, 2499, -1, 5162, -1, 7583, -1], 'generators': [83464080, 5875397673], 'label': '21600.y.3600.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '3600.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947803
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.i1.a1', '720.m1.a1', '1200.h1.a1', '1200.k1.a1', '1800.e1.b1', '1800.h1.a1', '1800.k1.b1', '1800.bb1.a1', '1800.bb1.a2', '1800.bd1.a1'], 'contains': ['7200.a1.a1', '10800.c1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6398, -1, 2761, -1, 5483, -1, 6739, -1], 'generators': [43545600, 5316889264], 'label': '21600.y.3600.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '3600.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947804
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.i1.b1', '720.m1.b1', '1200.h1.b1', '1200.k1.b1', '1800.e1.a1', '1800.h1.b1', '1800.k1.a1', '1800.bb1.b1', '1800.bb1.b2', '1800.bd1.a1'], 'contains': ['7200.a1.a1', '10800.c1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6398, -1, 2153, -1, 5483, -1, 6607, -1], 'generators': [43545600, 39918480], 'label': '21600.y.3600.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '3600.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947805
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.j1.a1', '1200.j1.a1', '1200.k1.a1', '1800.b1.b1', '1800.i1.a1', '1800.bc1.b1'], 'contains': ['7200.b1.b1', '10800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6473, -1, 1974, -1, 4965, -1, 7560, -1], 'generators': [5832138543, 5312972313], 'label': '21600.y.3600.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '3600.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947806
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '180.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.j1.b1', '1200.j1.b1', '1200.k1.b1', '1800.b1.a1', '1800.i1.b1', '1800.bc1.a1'], 'contains': ['7200.b1.a1', '10800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6473, -1, 5629, -1, 4965, -1, 7742, -1], 'generators': [10080, 83467464], 'label': '21600.y.3600.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '3600.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947807
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.k1.a1', '1200.i1.a1', '1200.k1.a1', '1800.j1.a1'], 'contains': ['7200.c1.a1', '10800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6130, -1, 4865, -1, 4880, -1, 5566, -1], 'generators': [5832138543, 5356517913], 'label': '21600.y.3600.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '3600.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947808
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.k1.b1', '1200.i1.b1', '1200.k1.b1', '1800.j1.b1'], 'contains': ['7200.c1.b1', '10800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6130, -1, 7027, -1, 4880, -1, 6208, -1], 'generators': [83467464, 79843680], 'label': '21600.y.3600.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.b1', 'old_label': '3600.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947809
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '30.b1.b1'], 'contains': ['120.f1.b1', '180.i1.b1', '180.j1.b1', '240.e1.b1', '300.j1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6235, -1, 6962, -1, 3970, -1, 3668, -1], 'generators': [4877764140, 43545600, 2039754482, 2003708310, 1959914882, 5396700062], 'label': '21600.y.60.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '60.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.b1', 'subgroup_fusion': None, 'weyl_group': '720.797'}
  • id: 63947810
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '450.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.n1.a1', '720.n1.b1', '720.o1.a1', '720.o1.b1', '1200.l1.a1', '1200.l1.b1', '1200.m1.a1', '1800.f1.a1', '1800.l1.a1', '1800.l1.b1', '1800.q1.a1', '1800.bb1.a1', '1800.bb1.a2', '1800.bb1.b1', '1800.bb1.b2', '1800.bd1.a1', '1800.be1.a1', '1800.be1.a2', '1800.bf1.a1', '1800.bf1.a2'], 'contains': ['7200.a1.a1', '10800.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [6056, -1, 4919, -1, 7033, -1, 6921, -1], 'generators': [43545600, 5356807744], 'label': '21600.y.3600.l1.a1', 'mobius_quo': None, 'mobius_sub': 32, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '3600.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947811
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.p1.a1', '1200.l1.a1', '1200.n1.a1', '1800.c1.a1', '1800.m1.b1', '1800.z1.b1', '1800.ba1.a1', '1800.ba1.a2', '1800.bc1.a1'], 'contains': ['7200.b1.a1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6093, -1, 7964, -1, 5998, -1, 7845, -1], 'generators': [4834223604, 10080], 'label': '21600.y.3600.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.a1', 'old_label': '3600.m1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947812
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '900.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.p1.b1', '1200.l1.b1', '1200.n1.a1', '1800.c1.b1', '1800.m1.a1', '1800.z1.a1', '1800.ba1.b1', '1800.ba1.b2', '1800.bc1.b1'], 'contains': ['7200.b1.b1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [6093, -1, 4699, -1, 5998, -1, 7674, -1], 'generators': [5792223423, 5312972313], 'label': '21600.y.3600.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.c1.b1', 'old_label': '3600.m1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947814
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1350.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.q1.a1', '720.q1.b1', '720.r1.a1', '720.r1.b1', '1200.o1.a1', '1200.o1.b1', '1200.p1.a1', '1800.f1.a1', '1800.h1.a1', '1800.h1.b1', '1800.n1.a1', '1800.n1.b1', '1800.bb1.a1', '1800.bb1.a2', '1800.bb1.b1', '1800.bb1.b2', '1800.be1.a1', '1800.be1.a2'], 'contains': ['7200.a1.a1', '10800.e1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [6360, -1, 3470, -1, 6820, -1, 6806, -1], 'generators': [5316890944, 43545600], 'label': '21600.y.3600.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '3600.o1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947815
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.s1.a1', '1200.o1.a1', '1200.q1.a1', '1200.r1.a1', '1800.c1.a1', '1800.i1.b1', '1800.o1.b1', '1800.r1.a1', '1800.ba1.a1', '1800.ba1.a2'], 'contains': ['7200.b1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [5993, -1, 7389, -1, 6044, -1, 7799, -1], 'generators': [10080, 4837852404], 'label': '21600.y.3600.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.a1', 'old_label': '3600.p1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947816
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2700.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.s1.b1', '1200.o1.b1', '1200.q1.b1', '1200.r1.a1', '1800.c1.b1', '1800.i1.a1', '1800.o1.a1', '1800.r1.b1', '1800.ba1.b1', '1800.ba1.b2'], 'contains': ['7200.b1.b1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [5993, -1, 3068, -1, 6044, -1, 7628, -1], 'generators': [5832140223, 5312972313], 'label': '21600.y.3600.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '450.b1.b1', 'old_label': '3600.p1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.p1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947817
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.t1.a1', '1200.o1.b1', '1200.q1.a1', '1200.s1.a1', '1800.j1.a1', '1800.p1.a1'], 'contains': ['7200.c1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [5833, -1, 6587, -1, 6313, -1, 5595, -1], 'generators': [5832140223, 5356517913], 'label': '21600.y.3600.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.t1.a1', 'old_label': '3600.q1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947818
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.t1.b1', '1200.o1.a1', '1200.q1.b1', '1200.s1.a1', '1800.j1.b1', '1800.p1.b1'], 'contains': ['7200.c1.b1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 900, 'diagramx': [5833, -1, 7829, -1, 6313, -1, 6230, -1], 'generators': [79843680, 4837852404], 'label': '21600.y.3600.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '900.t1.b1', 'old_label': '3600.q1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.q1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947819
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1200.p1.a1', '1200.r1.a1', '1200.s1.a1', '1800.d1.a1'], 'contains': ['7200.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1800, 'diagramx': [6911, -1, 7848, -1, 8063, -1, 7961, -1], 'generators': [15988, 1999848361], 'label': '21600.y.3600.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1800.d1.a1', 'old_label': '3600.r1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947820
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '12.c1.b1', '30.b1.a1'], 'contains': ['120.f1.a1', '180.l1.a1', '180.m1.a1', '180.n1.a1', '240.c1.b1', '300.o1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2035, -1, 5657, -1, 4416, -1, 1842, -1], 'generators': [5872055580, 43545600, 4914092461, 2424, 79834440, 1680], 'label': '21600.y.60.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.g1.a1', 'projective_image': '21600.y', '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': '240.198'}
  • id: 63947821
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '3600.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1200.p1.a1', '1200.q1.a1', '1200.q1.b1', '1200.s1.a1'], 'contains': ['7200.e1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 3600, 'diagramx': [6294, -1, 7866, -1, 7939, -1, 6276, -1], 'generators': [1999848361, 43561588], 'label': '21600.y.3600.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3600.s1.a1', 'old_label': '3600.s1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3600.s1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 63947822
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '4320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1.a1', '1440.a1.a1', '1440.c1.a1', '1440.d1.b1', '2160.a1.a1', '2160.c1.a1', '2160.d1.b1', '2160.e1.b1', '2160.f1.a1', '2160.g1.a1', '2160.i1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8052, -1, 1439, -1, 2419, -1, 2003, -1], 'generators': [5792221740], 'label': '21600.y.4320.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '4320.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947823
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '4320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1.a1', '1440.a1.b1', '1440.c1.b1', '1440.d1.a1', '2160.a1.b1', '2160.c1.b1', '2160.d1.a1', '2160.e1.a1', '2160.f1.b1', '2160.g1.b1', '2160.i1.b1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8052, -1, 879, -1, 2419, -1, 4044, -1], 'generators': [6000], 'label': '21600.y.4320.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '4320.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947824
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '4320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1.a1', '1440.b1.a1', '2160.b1.a1', '2160.h1.a1', '2160.j1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9570, -1, 783, -1, 3891, -1, 2502, -1], 'generators': [4833942753], 'label': '21600.y.4320.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '4320.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947825
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '4320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1.a1', '1440.b1.b1', '2160.b1.b1', '2160.h1.b1', '2160.j1.b1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9570, -1, 675, -1, 3891, -1, 2656, -1], 'generators': [5792274422], 'label': '21600.y.4320.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '4320.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947826
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.a1.a1', '1080.b1.a1', '1800.a1.a1', '1800.b1.a1', '1800.e1.a1', '2700.a1.a1', '2700.b1.a1', '2700.c1.a1'], 'contains': ['10800.a1.a1', '10800.b1.a1', '10800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6999, -1, 3573, -1, 5530, -1, 7986, -1], 'generators': [39916800, 1680], 'label': '21600.y.5400.a1.a1', 'mobius_quo': None, 'mobius_sub': 240, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '5400.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947827
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.a1.b1', '1080.b1.b1', '1800.a1.b1', '1800.b1.b1', '1800.e1.b1', '2700.a1.b1', '2700.b1.a1', '2700.c1.b1'], 'contains': ['10800.a1.a1', '10800.b1.b1', '10800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6999, -1, 3755, -1, 5530, -1, 8012, -1], 'generators': [39916800, 5313260464], 'label': '21600.y.5400.a1.b1', 'mobius_quo': None, 'mobius_sub': 240, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.b1', 'old_label': '5400.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947828
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.c1.a1', '1080.c1.b1', '1080.d1.a1', '1080.d1.b1', '1800.c1.a1', '1800.c1.b1', '1800.d1.a1', '1800.f1.a1', '2700.a1.a1', '2700.a1.b1', '2700.b1.a1', '2700.d1.a1', '2700.d1.a2'], 'contains': ['10800.a1.a1', '10800.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [7545, -1, 4684, -1, 6866, -1, 8063, -1], 'generators': [3628800, 5316890944], 'label': '21600.y.5400.b1.a1', 'mobius_quo': None, 'mobius_sub': 32, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947829
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.f1.a1', '1080.j1.a1', '1800.h1.a1', '1800.i1.a1', '1800.j1.a1', '1800.r1.a1', '2700.b1.a1', '2700.e1.a1', '2700.e1.a2', '2700.f1.a1', '2700.g1.a1', '2700.j1.a1'], 'contains': ['10800.b1.a1', '10800.c1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [5698, -1, 4636, -1, 6410, -1, 8264, -1], 'generators': [1680, 5316889264], 'label': '21600.y.5400.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947830
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.f1.b1', '1080.j1.b1', '1800.h1.b1', '1800.i1.b1', '1800.j1.b1', '1800.r1.b1', '2700.b1.a1', '2700.e1.b1', '2700.e1.b2', '2700.f1.b1', '2700.g1.b1', '2700.j1.b1'], 'contains': ['10800.b1.b1', '10800.c1.b1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [5698, -1, 4846, -1, 6410, -1, 8212, -1], 'generators': [5313260464, 39918480], 'label': '21600.y.5400.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947831
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '12.c1.a1', '30.b1.b1'], 'contains': ['120.f1.b1', '180.l1.b1', '180.m1.b1', '180.n1.b1', '240.c1.a1', '300.o1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2035, -1, 7375, -1, 4416, -1, 3609, -1], 'generators': [4877764140, 43545600, 2039754482, 2003708310, 5393071262, 1959914882], 'label': '21600.y.60.g1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.b1', 'old_label': '60.g1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.b1', 'subgroup_fusion': None, 'weyl_group': '240.198'}
  • id: 63947832
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.e1.a1', '1800.g1.a1', '1800.k1.a1', '2700.c1.a1', '2700.f1.a1', '2700.g1.b1'], 'contains': ['10800.b1.a1', '10800.c1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4001, -1, 3795, -1, 6174, -1, 8186, -1], 'generators': [2424, 39918480], 'label': '21600.y.5400.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '5400.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947833
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.e1.b1', '1800.g1.b1', '1800.k1.b1', '2700.c1.b1', '2700.f1.b1', '2700.g1.a1'], 'contains': ['10800.b1.b1', '10800.c1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [4001, -1, 7061, -1, 6174, -1, 8290, -1], 'generators': [5316889264, 5792262065], 'label': '21600.y.5400.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.b1', 'old_label': '5400.d1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947834
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.g1.a1', '1800.l1.a1', '1800.m1.a1', '2700.a1.a1', '2700.e1.a1', '2700.e1.a2', '2700.f1.a1', '2700.i1.a1', '2700.k1.b1'], 'contains': ['10800.b1.a1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2148, -1, 6778, -1, 7326, -1, 8765, -1], 'generators': [1680, 5313262888], 'label': '21600.y.5400.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '5400.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947835
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.g1.b1', '1800.l1.b1', '1800.m1.b1', '2700.a1.b1', '2700.e1.b1', '2700.e1.b2', '2700.f1.b1', '2700.i1.a1', '2700.k1.a1'], 'contains': ['10800.b1.b1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [2148, -1, 7858, -1, 7326, -1, 8842, -1], 'generators': [5313260464, 5792263745], 'label': '21600.y.5400.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '5400.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947836
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.h1.a1', '1800.n1.a1', '1800.o1.a1', '1800.p1.a1', '2700.a1.a1', '2700.e1.a1', '2700.e1.a2', '2700.g1.b1', '2700.h1.a1', '2700.j1.a1'], 'contains': ['10800.b1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2711, -1, 4876, -1, 6936, -1, 8342, -1], 'generators': [5316891688, 1680], 'label': '21600.y.5400.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.f1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947837
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.h1.b1', '1800.n1.b1', '1800.o1.b1', '1800.p1.b1', '2700.a1.b1', '2700.e1.b1', '2700.e1.b2', '2700.g1.a1', '2700.h1.a1', '2700.j1.b1'], 'contains': ['10800.b1.b1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2711, -1, 7100, -1, 6936, -1, 8423, -1], 'generators': [5875726145, 5313260464], 'label': '21600.y.5400.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.f1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947838
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.k1.a1', '1080.k1.b1', '1800.q1.a1', '1800.z1.a1', '1800.z1.b1', '2700.b1.a1', '2700.g1.a1', '2700.g1.b1', '2700.h1.a1', '2700.i1.a1', '2700.k1.a1', '2700.k1.b1'], 'contains': ['10800.b1.a1', '10800.b1.b1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [1619, -1, 7817, -1, 7255, -1, 8316, -1], 'generators': [5313260464, 1680], 'label': '21600.y.5400.g1.a1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '5400.g1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947839
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.i1.a1', '1800.s1.a1', '1800.t1.a1', '1800.u1.a1', '1800.v1.a1', '1800.w1.a1', '1800.x1.a1', '1800.y1.a1', '2700.c1.a1', '2700.j1.a1', '2700.k1.b1'], 'contains': ['10800.b1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1868, -1, 7606, -1, 7120, -1, 8037, -1], 'generators': [2424, 1680], 'label': '21600.y.5400.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5400.h1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.h1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947840
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.i1.b1', '1800.s1.b1', '1800.t1.b1', '1800.u1.b1', '1800.v1.b1', '1800.w1.b1', '1800.x1.b1', '1800.y1.b1', '2700.c1.b1', '2700.j1.b1', '2700.k1.a1'], 'contains': ['10800.b1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1868, -1, 8611, -1, 7120, -1, 8089, -1], 'generators': [5313260464, 5792262065], 'label': '21600.y.5400.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '5400.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.h1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947841
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.l1.a1', '1800.ba1.a1', '1800.bb1.a1', '2700.a1.b1', '2700.e1.a2', '2700.f1.b1', '2700.g1.a1', '2700.l1.a1', '2700.l1.a2'], 'contains': ['10800.c1.a1', '10800.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2554, -1, 6436, -1, 6986, -1, 8791, -1], 'generators': [5795892545, 5316889264], 'label': '21600.y.5400.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.i1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947842
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.c1.b1', '30.d1.b1'], 'contains': ['120.a1.a1', '180.o1.a1', '300.j1.a1', '360.q1.a1', '600.k1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5433, -1, 6763, -1, 3857, -1, 3879, -1], 'generators': [4837853940, 43545600, 4837858164, 4837847340], 'label': '21600.y.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '60.h1.a1', 'projective_image': '21600.y', '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': '360.121'}
  • id: 63947843
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.l1.a2', '1800.ba1.a2', '1800.bb1.a2', '2700.a1.b1', '2700.e1.a1', '2700.f1.b1', '2700.g1.a1', '2700.l1.a1', '2700.l1.a2'], 'contains': ['10800.c1.a1', '10800.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2554, -1, 6353, -1, 6986, -1, 8817, -1], 'generators': [5792263745, 5316889264], 'label': '21600.y.5400.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.i1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.i1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947844
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.l1.b1', '1800.ba1.b1', '1800.bb1.b1', '2700.a1.a1', '2700.e1.b1', '2700.f1.a1', '2700.g1.b1', '2700.l1.a1', '2700.l1.a2'], 'contains': ['10800.c1.b1', '10800.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2554, -1, 3945, -1, 6986, -1, 8558, -1], 'generators': [5316891688, 3630480], 'label': '21600.y.5400.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947845
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.l1.b2', '1800.ba1.b2', '1800.bb1.b2', '2700.a1.a1', '2700.e1.b2', '2700.f1.a1', '2700.g1.b1', '2700.l1.a1', '2700.l1.a2'], 'contains': ['10800.c1.b1', '10800.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [2554, -1, 4014, -1, 6986, -1, 8639, -1], 'generators': [39918480, 5313262888], 'label': '21600.y.5400.i1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.i1.b2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.i1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947846
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1080.m1.a1', '1080.m1.b1', '1800.bc1.a1', '1800.bc1.b1', '1800.bd1.a1', '2700.b1.a1', '2700.f1.a1', '2700.f1.b1', '2700.l1.a1', '2700.l1.a2'], 'contains': ['10800.c1.a1', '10800.c1.b1', '10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [7129, -1, 3857, -1, 6360, -1, 8238, -1], 'generators': [5316889264, 3630480], 'label': '21600.y.5400.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.j1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947847
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.be1.a1', '2700.d1.a1', '2700.e1.a1', '2700.e1.a2', '2700.e1.b1', '2700.e1.b2', '2700.h1.a1', '2700.l1.a2'], 'contains': ['10800.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [702, -1, 6683, -1, 7985, -1, 9098, -1], 'generators': [5316891688, 5792263745], 'label': '21600.y.5400.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.k1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947848
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.be1.a2', '2700.d1.a2', '2700.e1.a1', '2700.e1.a2', '2700.e1.b1', '2700.e1.b2', '2700.h1.a1', '2700.l1.a1'], 'contains': ['10800.d1.a1', '10800.e1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [702, -1, 6712, -1, 7985, -1, 9124, -1], 'generators': [5316890008, 5792263745], 'label': '21600.y.5400.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '5400.k1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.k1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947849
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bf1.a1', '1800.bg1.a1', '1800.bh1.a2', '2700.d1.a1', '2700.i1.a1', '2700.l1.a1'], 'contains': ['10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1577, -1, 8056, -1, 8464, -1, 8894, -1], 'generators': [5792263745, 5313262888], 'label': '21600.y.5400.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a2', 'old_label': '5400.l1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.l1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947850
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '5400.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.bf1.a2', '1800.bg1.a2', '1800.bh1.a1', '2700.d1.a2', '2700.i1.a1', '2700.l1.a2'], 'contains': ['10800.d1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1577, -1, 7888, -1, 8464, -1, 8868, -1], 'generators': [5792263745, 5313261208], 'label': '21600.y.5400.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '5400.l1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5400.l1.a2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 63947851
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '7200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1440.a1.a1', '1440.a1.b1', '1440.b1.a1', '1440.b1.b1', '2400.a1.a1', '2400.a1.b1', '2400.b1.a1', '3600.a1.a1', '3600.d1.a1', '3600.d1.b1', '3600.i1.a1', '3600.i1.b1', '3600.l1.a1', '3600.o1.a1'], 'contains': ['21600.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6219, 5159, 2019, 5747, 5937, 6546, 6519, 6289], 'generators': [43545600], 'label': '21600.y.7200.a1.a1', 'mobius_quo': -1, 'mobius_sub': -10800, 'normal_closure': '7200.a1.a1', 'normal_contained_in': ['120.a1.a1', '120.a1.b1', '3600.a1.a1'], 'normal_contains': ['21600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '7200.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3600.a', 'quotient_action_kernel_order': 3600, 'quotient_fusion': None, 'short_label': '7200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947852
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '7200.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.c1.a1', '1800.u1.a1', '2400.a1.a1', '2400.c1.a1', '2400.d1.a1', '3600.b1.a1', '3600.e1.b1', '3600.g1.a1', '3600.h1.a1', '3600.j1.b1', '3600.m1.a1', '3600.p1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5638, -1, 7689, -1, 5824, -1, 7719, -1], 'generators': [840], 'label': '21600.y.7200.b1.a1', 'mobius_quo': None, 'mobius_sub': -360, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '7200.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7200.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947853
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '20.b1.b1', '30.c1.a1', '30.d1.a1'], 'contains': ['120.a1.b1', '180.o1.b1', '300.j1.b1', '360.q1.b1', '600.k1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [5433, -1, 5017, -1, 3857, -1, 2143, -1], 'generators': [5795604391, 43545600, 5396684222, 39918480], 'label': '21600.y.60.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.h1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947854
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '7200.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.c1.b1', '1800.u1.b1', '2400.a1.b1', '2400.c1.b1', '2400.d1.a1', '3600.b1.b1', '3600.e1.a1', '3600.g1.b1', '3600.h1.b1', '3600.j1.a1', '3600.m1.b1', '3600.p1.b1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5638, -1, 3667, -1, 5824, -1, 7537, -1], 'generators': [5791933593], 'label': '21600.y.7200.b1.b1', 'mobius_quo': None, 'mobius_sub': -360, 'normal_closure': '360.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '7200.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7200.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947855
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '7200.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.d1.a1', '1800.w1.b1', '2400.a1.b1', '2400.c1.a1', '2400.e1.a1', '3600.f1.a1', '3600.k1.a1', '3600.q1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5393, -1, 6910, -1, 6223, -1, 5542, -1], 'generators': [5871767193], 'label': '21600.y.7200.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '7200.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7200.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947856
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '7200.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.d1.b1', '1800.w1.a1', '2400.a1.a1', '2400.c1.b1', '2400.e1.a1', '3600.f1.b1', '3600.k1.b1', '3600.q1.b1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5393, -1, 8501, -1, 6223, -1, 6183, -1], 'generators': [79834440], 'label': '21600.y.7200.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.b1', 'old_label': '7200.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7200.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947857
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '7200.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.x1.a1', '1800.x1.b1', '1800.bg1.a1', '1800.bg1.a2', '2400.b1.a1', '2400.d1.a1', '2400.e1.a1', '3600.c1.a1', '3600.n1.a1', '3600.r1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [4737, -1, 9605, -1, 8201, -1, 7869, -1], 'generators': [5791933737], 'label': '21600.y.7200.d1.a1', 'mobius_quo': None, 'mobius_sub': -36, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.b1.a1', 'old_label': '7200.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7200.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947858
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '7200.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1800.y1.a1', '1800.y1.b1', '1800.bh1.a1', '1800.bh1.a2', '2400.b1.a1', '2400.c1.a1', '2400.c1.b1', '2400.e1.a1', '3600.s1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 400, 'diagramx': [4413, -1, 9702, -1, 8109, -1, 7765, -1], 'generators': [5871767337], 'label': '21600.y.7200.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '400.e1.a1', 'old_label': '7200.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7200.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63947859
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.a1.a1', '2160.a1.b1', '2160.b1.a1', '2160.b1.b1', '3600.a1.a1', '3600.b1.a1', '3600.b1.b1', '3600.c1.a1', '5400.a1.a1', '5400.a1.b1', '5400.b1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7494, -1, 1200, -1, 5552, -1, 7742, -1], 'generators': [39916800], 'label': '21600.y.10800.a1.a1', 'mobius_quo': None, 'mobius_sub': -10800, 'normal_closure': '3600.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '10800.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947860
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.c1.a1', '2160.d1.a1', '3600.d1.a1', '3600.e1.a1', '3600.f1.a1', '3600.g1.a1', '5400.a1.a1', '5400.c1.a1', '5400.d1.a1', '5400.e1.a1', '5400.f1.a1', '5400.g1.a1', '5400.h1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4131, -1, 4806, -1, 6268, -1, 7915, -1], 'generators': [1680], 'label': '21600.y.10800.b1.a1', 'mobius_quo': None, 'mobius_sub': -720, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '10800.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947861
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.c1.b1', '2160.d1.b1', '3600.d1.b1', '3600.e1.b1', '3600.f1.b1', '3600.g1.b1', '5400.a1.b1', '5400.c1.b1', '5400.d1.b1', '5400.e1.b1', '5400.f1.b1', '5400.g1.a1', '5400.h1.b1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4131, -1, 7766, -1, 6268, -1, 7960, -1], 'generators': [5313260464], 'label': '21600.y.10800.b1.b1', 'mobius_quo': None, 'mobius_sub': -720, 'normal_closure': '360.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '10800.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947862
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10800.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.e1.a1', '2160.f1.a1', '3600.h1.a1', '3600.i1.a1', '3600.j1.a1', '3600.k1.a1', '5400.a1.b1', '5400.c1.a1', '5400.d1.b1', '5400.i1.a1', '5400.i1.a2', '5400.j1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6157, -1, 4636, -1, 5496, -1, 7937, -1], 'generators': [5316889264], 'label': '21600.y.10800.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.b1', 'old_label': '10800.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947863
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10800.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.e1.b1', '2160.f1.b1', '3600.h1.b1', '3600.i1.b1', '3600.j1.b1', '3600.k1.b1', '5400.a1.a1', '5400.c1.b1', '5400.d1.a1', '5400.i1.b1', '5400.i1.b2', '5400.j1.a1'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [6157, -1, 3739, -1, 5496, -1, 7892, -1], 'generators': [39918480], 'label': '21600.y.10800.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '10800.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947864
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['120.i1.a1', '180.o1.a1', '300.k1.a1', '360.s1.a1', '600.l1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5285, -1, 6881, -1, 4621, -1, 4140, -1], 'generators': [5832138543, 1584, 80081432, 21744], 'label': '21600.y.60.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.a1', 'old_label': '60.i1.a1', 'projective_image': '21600.y', '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': '360.121'}
  • id: 63947865
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10800.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '225.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.g1.a1', '2160.g1.b1', '2160.h1.a1', '2160.h1.b1', '3600.l1.a1', '3600.m1.a1', '3600.m1.b1', '3600.n1.a1', '5400.b1.a1', '5400.e1.a1', '5400.e1.b1', '5400.g1.a1', '5400.i1.a1', '5400.i1.a2', '5400.i1.b1', '5400.i1.b2', '5400.j1.a1', '5400.k1.a1', '5400.k1.a2', '5400.l1.a1', '5400.l1.a2'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [5948, -1, 6755, -1, 6986, -1, 8277, -1], 'generators': [5313262144], 'label': '21600.y.10800.d1.a1', 'mobius_quo': None, 'mobius_sub': -96, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.c1.a1', 'old_label': '10800.d1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947866
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10800.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '675.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2160.i1.a1', '2160.i1.b1', '2160.j1.a1', '2160.j1.b1', '3600.o1.a1', '3600.p1.a1', '3600.p1.b1', '3600.q1.a1', '3600.q1.b1', '3600.r1.a1', '3600.s1.a1', '5400.b1.a1', '5400.c1.a1', '5400.c1.b1', '5400.f1.a1', '5400.f1.b1', '5400.i1.a1', '5400.i1.a2', '5400.i1.b1', '5400.i1.b2', '5400.k1.a1', '5400.k1.a2'], 'contains': ['21600.a1.a1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 675, 'diagramx': [6008, -1, 4788, -1, 6820, -1, 7983, -1], 'generators': [5316890944], 'label': '21600.y.10800.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '675.a1.a1', 'old_label': '10800.e1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10800.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947867
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '21600.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': ['4320.a1.a1', '4320.a1.b1', '4320.b1.a1', '4320.b1.b1', '7200.a1.a1', '7200.b1.a1', '7200.b1.b1', '7200.c1.a1', '7200.c1.b1', '7200.d1.a1', '7200.e1.a1', '10800.a1.a1', '10800.b1.a1', '10800.b1.b1', '10800.c1.a1', '10800.c1.b1', '10800.d1.a1', '10800.e1.a1'], 'contains': [], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5977, 3932, 4713, 3933, 6070, 5236, 7731, 4639], 'generators': [], 'label': '21600.y.21600.a1.a1', 'mobius_quo': 1, 'mobius_sub': 32400, 'normal_closure': '21600.a1.a1', 'normal_contained_in': ['360.a1.a1', '360.a1.b1', '7200.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '21600.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63947868
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.b1'], 'contains': ['120.i1.b1', '180.o1.b1', '300.k1.b1', '360.s1.b1', '600.l1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 60, 'diagramx': [5285, -1, 8142, -1, 4621, -1, 2373, -1], 'generators': [2003481482, 83479080, 79849584, 80137737], 'label': '21600.y.60.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.i1.b1', 'old_label': '60.i1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947869
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.b1', '18.a1.b1', '30.b1.a1', '30.c1.b1', '36.b1.a1', '60.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5991, -1, 3984, -1, 3059, -1, 1937, -1], 'generators': [4877766324, 2043377285, 39916800, 43545600, 5832178862, 4877775660], 'label': '21600.y.6.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '6.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '3600.de'}
  • id: 63947870
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '30.a1.b1'], 'contains': ['120.j1.a1', '180.o1.a1', '300.l1.a1', '360.r1.a1', '600.m1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5512, -1, 6846, -1, 4797, -1, 4328, -1], 'generators': [5832138543, 247832, 1584, 21744], 'label': '21600.y.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.b1', 'old_label': '60.j1.a1', 'projective_image': '21600.y', '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': '360.121'}
  • id: 63947871
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.b1', '30.a1.a1'], 'contains': ['120.j1.b1', '180.o1.b1', '300.l1.b1', '360.r1.b1', '600.m1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 30, 'diagramx': [5512, -1, 5354, -1, 4797, -1, 2561, -1], 'generators': [83479080, 304137, 1959935882, 15984], 'label': '21600.y.60.j1.b1', '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.j1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947872
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.c1.a1', '30.c1.a1', '30.d1.a1', '30.e1.a1'], 'contains': ['120.a1.b1', '180.p1.a1', '300.o1.a1', '360.t1.a1', '600.u1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [1868, -1, 5419, -1, 5148, -1, 2283, -1], 'generators': [43545600, 5393055422, 5835521191, 1680], 'label': '21600.y.60.k1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.k1.a1', 'projective_image': '21600.y', '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': '120.35'}
  • id: 63947873
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1800.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '20.c1.b1', '30.c1.b1', '30.d1.b1', '30.e1.b1'], 'contains': ['120.a1.a1', '180.p1.b1', '300.o1.b1', '360.t1.b1', '600.u1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1868, -1, 8395, -1, 5148, -1, 4050, -1], 'generators': [4877764140, 43545600, 4877770740, 4877774964], 'label': '21600.y.60.k1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.b1', 'old_label': '60.k1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947874
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '20.c1.a1', '30.a1.a1'], 'contains': ['120.j1.b1', '180.p1.a1', '300.r1.a1', '360.u1.a1', '600.v1.a1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [1678, -1, 7055, -1, 5370, -1, 2507, -1], 'generators': [304137, 16680, 1959935882, 15984], 'label': '21600.y.60.l1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '60.l1.a1', 'projective_image': '21600.y', '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': '360.121'}
  • id: 63947875
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '20.c1.b1', '30.a1.b1'], 'contains': ['120.j1.a1', '180.p1.b1', '300.r1.b1', '360.u1.b1', '600.v1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1678, -1, 8333, -1, 5370, -1, 4195, -1], 'generators': [247832, 1584, 21744, 5792221743], 'label': '21600.y.60.l1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '60.l1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.b1', 'subgroup_fusion': None, 'weyl_group': '360.121'}
  • id: 63947876
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '36.b1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.b1', '216.a1.a1', '360.e1.a1', '360.f1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8359, -1, 633, -1, 546, -1, 760, -1], 'generators': [39916800, 43545600, 5832178862, 5832200606, 12360], 'label': '21600.y.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.a1.a1', 'projective_image': '21600.y', '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': '120.42'}
  • id: 63947877
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '36.b1.a1'], 'contains': ['144.a1.a1', '144.b1.b1', '144.c1.a1', '216.a1.b1', '360.e1.b1', '360.f1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8359, -1, 1008, -1, 546, -1, 500, -1], 'generators': [2043377285, 39916800, 43545600, 5832178862, 12360], 'label': '21600.y.72.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.a1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.b1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
  • id: 63947878
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.e1.a1', '216.b1.a1', '360.g1.a1', '360.g1.b1', '360.h1.a1', '360.h1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9007, -1, 3009, -1, 902, -1, 913, -1], 'generators': [39916800, 43545600, 5832178862, 4837869084, 12360], 'label': '21600.y.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.b1.a1', 'projective_image': '21600.y', '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': '600.174'}
  • id: 63947879
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '36.b1.a1'], 'contains': ['144.b1.a1', '144.c1.a1', '144.e1.a1', '216.c1.a1', '360.j1.a1', '360.q1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8496, -1, 1793, -1, 683, -1, 700, -1], 'generators': [2043377285, 43545600, 5792262062, 4837869084, 12360], 'label': '21600.y.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '21600.y', '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': '600.174'}
  • id: 63947880
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.a1.b1', '20.b1.b1', '20.c1.a1', '30.a1.a1', '30.c1.a1', '50.a1.a1', '60.d1.a1', '100.b1.a1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [5394, -1, 6073, -1, 5095, -1, 2401, -1], 'generators': [83479080, 39916800, 43545600, 40220937, 2043398282, 83478384], 'label': '21600.y.10.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '21600.y', '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': '2160.cm'}
  • id: 63947881
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '36.b1.a1'], 'contains': ['144.b1.b1', '144.c1.b1', '144.e1.a1', '216.c1.b1', '360.j1.b1', '360.q1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8496, -1, 2320, -1, 683, -1, 429, -1], 'generators': [43545600, 2039748485, 5792262062, 4837869084, 12360], 'label': '21600.y.72.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.c1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': '600.174'}
  • id: 63947882
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.c1.b1', '36.b1.a1'], 'contains': ['144.b1.a1', '144.b1.b1', '144.d1.a1', '216.d1.a1', '360.t1.a1', '360.t1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7953, -1, 4889, -1, 803, -1, 378, -1], 'generators': [43545600, 4877785884, 2039748485, 5792262062, 12360], 'label': '21600.y.72.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '21600.y', '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': '200.49'}
  • id: 63947883
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.a1.a1', '36.c1.a1', '36.d1.b1'], 'contains': ['360.a1.a1', '360.o1.a1', '432.b1.a1', '720.e1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7016, -1, 3669, -1, 2630, -1, 815, -1], 'generators': [5792273582, 5792264246, 5792262062], 'label': '21600.y.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.b1', 'old_label': '72.e1.a1', 'projective_image': '21600.y', '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': '120.35'}
  • id: 63947884
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '36.a1.b1', '36.c1.b1', '36.d1.a1'], 'contains': ['360.a1.b1', '360.o1.b1', '432.b1.b1', '720.e1.b1'], 'core': '360.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7016, -1, 5874, -1, 2630, -1, 605, -1], 'generators': [10320, 269671, 5312931992], 'label': '21600.y.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.e1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.b1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 63947885
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1'], 'contains': ['144.c1.a1', '144.c1.b1', '144.d1.a1', '216.e1.a1', '360.x1.a1', '360.x1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8870, -1, 914, -1, 445, -1, 867, -1], 'generators': [2043377285, 43545600, 4877785884, 5792262062, 12360], 'label': '21600.y.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.f1.a1', 'projective_image': '21600.y', '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': '600.174'}
  • id: 63947886
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '75.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.a1.b1', '25.a1.a1'], 'contains': ['150.h1.a1', '225.a1.a1', '225.a1.b1', '225.b1.a1', '225.b1.a2', '300.a1.a1', '300.a1.b1'], 'core': '21600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [1545, -1, 7699, -1, 7061, -1, 8198, -1], 'generators': [5313260464, 5875396137, 5875724705, 2424, 1680, 83463240, 83462400], 'label': '21600.y.75.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '75.a1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 63947887
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '75.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.b1', '25.a1.a1'], 'contains': ['150.b1.b1', '150.d1.b1', '150.e1.a1', '225.a1.a1', '225.c1.a1', '300.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [1842, -1, 7536, -1, 6506, -1, 6311, -1], 'generators': [39916800, 5356806064, 43545600, 5832179105, 2424, 1680, 83463240], 'label': '21600.y.75.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '75.b1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.166'}
  • id: 63947888
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '75.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5400.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.a1', '25.a1.a1'], 'contains': ['150.b1.a1', '150.d1.a1', '150.e1.b1', '225.a1.b1', '225.c1.a1', '300.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [1842, -1, 6617, -1, 6506, -1, 5506, -1], 'generators': [39916800, 5791934337, 5356806064, 43545600, 2424, 1680, 5872097345], 'label': '21600.y.75.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '75.b1.b1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.b1.b1', 'subgroup_fusion': None, 'weyl_group': '216.166'}
  • id: 63947889
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '75.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['25.a1.a1'], 'contains': ['150.f1.a1', '225.b1.a1', '225.c1.a1', '300.f1.a1', '300.f1.b1', '300.h1.a2'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [1436, -1, 7884, -1, 9214, -1, 6852, -1], 'generators': [39916800, 5356806064, 43545600, 2424, 1680, 5791935177, 5872097345], 'label': '21600.y.75.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '75.c1.a1', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.c1.a1', 'subgroup_fusion': None, 'weyl_group': '864.4680'}
  • id: 63947890
    {'ambient': '21600.y', 'aut_centralizer_order': None, 'aut_label': '75.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['25.a1.a1'], 'contains': ['150.f1.a2', '225.b1.a2', '225.c1.a1', '300.f1.a1', '300.f1.b1', '300.h1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [1436, -1, 7115, -1, 9214, -1, 6793, -1], 'generators': [39916800, 5356806064, 43545600, 5875396137, 2424, 1680, 5872097345], 'label': '21600.y.75.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '75.c1.a2', 'projective_image': '21600.y', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.c1.a2', 'subgroup_fusion': None, 'weyl_group': '864.4680'}