Abstract group data - 7200.c

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 120, 'aut_gen_orders': [5, 2, 2], 'aut_gens': [[54980613645, 31953047400], [5867336140, 64868294299], [132769746010, 94128447418], [1713024755, 50770446436]], 'aut_group': '28800.r', 'aut_hash': 1736489480735889307, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 28800, 'aut_permdeg': 40, 'aut_perms': [535210959881647532, 1349707796299950773, 419312290351259882110423385360173573663450926958], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 450, 1, 1], [3, 20, 2, 1], [3, 400, 1, 1], [4, 30, 2, 1], [5, 12, 4, 1], [5, 144, 4, 1], [6, 20, 2, 1], [6, 400, 1, 1], [10, 12, 4, 1], [10, 144, 4, 1], [12, 600, 2, 1], [15, 240, 4, 1], [20, 360, 4, 1], [30, 240, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_5\\wr C_2', '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': '28800.r', 'autcentquo_hash': 1736489480735889307, 'autcentquo_nilpotent': False, 'autcentquo_order': 28800, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_5\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 450, 1], [3, 20, 2], [3, 400, 1], [4, 30, 2], [5, 12, 4], [5, 144, 4], [6, 20, 2], [6, 400, 1], [10, 12, 4], [10, 144, 4], [12, 600, 2], [15, 240, 4], [20, 360, 4], [30, 240, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '3600.a', 'commutator_count': 1, 'commutator_label': '7200.c', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '60.5', '60.5'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 450, 1, 1], [3, 20, 1, 2], [3, 400, 1, 1], [4, 30, 1, 2], [5, 12, 2, 2], [5, 144, 2, 2], [6, 20, 1, 2], [6, 400, 1, 1], [10, 12, 2, 2], [10, 144, 2, 2], [12, 600, 1, 2], [15, 240, 2, 2], [20, 360, 2, 2], [30, 240, 2, 2]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 684, 'exponent': 60, 'exponents_of_order': [5, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 1, 4], [8, 1, 4], [12, 1, 4], [16, 1, 1], [24, 1, 2], [36, 1, 1]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '3600.a', 'hash': 5216169401806534062, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [15, 15], 'inner_gens': [[54980613645, 13378157173], [4644373423, 31953047400]], 'inner_hash': 8673234499945238871, 'inner_nilpotent': False, 'inner_order': 3600, 'inner_split': True, 'inner_tex': 'A_5^2', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 1], [3, 4], [4, 6], [5, 2], [8, 4], [9, 4], [12, 8], [15, 4], [16, 2], [20, 2], [24, 2], [25, 1], [36, 1]], 'label': '7200.c', 'linC_count': 4, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'Omega+(4,5)', 'ngens': 2, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 41, 'number_divisions': 27, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 85, 'number_subgroup_classes': 150, 'number_subgroups': 14896, 'old_label': None, 'order': 7200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 451], [3, 440], [4, 60], [5, 624], [6, 440], [10, 624], [12, 1200], [15, 960], [20, 1440], [30, 960]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [96556331409, 143286937975], 'outer_gens': [[12808986266, 94222197283], [119441764635, 71205645358]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [7, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': None, 'perfect': True, 'permutation_degree': 120, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 2], [5, 2], [6, 2], [8, 2], [16, 4], [18, 2], [20, 2], [24, 6], [25, 1], [30, 2], [36, 1]], 'representations': {'Lie': [{'d': 4, 'q': 5, 'gens': [31953047400, 54980613645], 'family': 'OmegaPlus'}], 'Perm': {'d': 120, 'gens': [112913124156197286813948428470476551306257844419999062007172767957806017286725478517115373111560619403224605805211661234135859857504661187252531434806469885032395353135881764806411411753718668850907, 56694809795822705453808600235045702423329178110486109608527457755126997586347243525062977232381905607962661033640162771186773293949899954095210711578646610090761461339448581957171323096446201394907]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\OmegaPlus(4,5)', 'transitive_degree': 120, '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: 110869590
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 3, 'group_order': 7200, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 30527346876, 'size': 1}
  • id: 110869601
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 3, 'group_order': 7200, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 122109387504, 'size': 1}
  • id: 110869612
    {'aut_label': '2B', 'centralizer': '450.b1.a1', 'counter': 3, 'group_counter': 3, 'group_order': 7200, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 35441028126, 'size': 450}
  • id: 110869623
    {'aut_label': '3A', 'centralizer': '20.a1.a1', 'counter': 4, 'group_counter': 3, 'group_order': 7200, 'label': '3A', 'order': 3, 'powers': [4, 1, 4], 'representative': 42802739398, 'size': 20}
  • id: 110869626
    {'aut_label': '3A', 'centralizer': '20.a1.b1', 'counter': 5, 'group_counter': 3, 'group_order': 7200, 'label': '3B', 'order': 3, 'powers': [5, 1, 5], 'representative': 3663137554, 'size': 20}
  • id: 110869627
    {'aut_label': '3C', 'centralizer': '400.a1.a1', 'counter': 6, 'group_counter': 3, 'group_order': 7200, 'label': '3C', 'order': 3, 'powers': [6, 1, 6], 'representative': 54650962212, 'size': 400}
  • id: 110869628
    {'aut_label': '4A', 'centralizer': '30.b1.a1', 'counter': 7, 'group_counter': 3, 'group_order': 7200, 'label': '4A', 'order': 4, 'powers': [2, 7, 7], 'representative': 91582350027, 'size': 30}
  • id: 110869629
    {'aut_label': '4A', 'centralizer': '30.b1.b1', 'counter': 8, 'group_counter': 3, 'group_order': 7200, 'label': '4B', 'order': 4, 'powers': [2, 8, 8], 'representative': 73271492503, 'size': 30}
  • id: 110869630
    {'aut_label': '5A1', 'centralizer': '12.a1.b1', 'counter': 9, 'group_counter': 3, 'group_order': 7200, 'label': '5A1', 'order': 5, 'powers': [10, 10, 1], 'representative': 67333993130, 'size': 12}
  • id: 110869591
    {'aut_label': '5A1', 'centralizer': '12.a1.b1', 'counter': 10, 'group_counter': 3, 'group_order': 7200, 'label': '5A2', 'order': 5, 'powers': [9, 9, 1], 'representative': 103945323764, 'size': 12}
  • id: 110869592
    {'aut_label': '5A1', 'centralizer': '12.a1.a1', 'counter': 11, 'group_counter': 3, 'group_order': 7200, 'label': '5B1', 'order': 5, 'powers': [12, 12, 1], 'representative': 94024856304, 'size': 12}
  • id: 110869593
    {'aut_label': '5A1', 'centralizer': '12.a1.a1', 'counter': 12, 'group_counter': 3, 'group_order': 7200, 'label': '5B2', 'order': 5, 'powers': [11, 11, 1], 'representative': 4883287602, 'size': 12}
  • id: 110869594
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 13, 'group_counter': 3, 'group_order': 7200, 'label': '5C1', 'order': 5, 'powers': [14, 14, 1], 'representative': 494954209, 'size': 144}
  • id: 110869595
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 14, 'group_counter': 3, 'group_order': 7200, 'label': '5C2', 'order': 5, 'powers': [13, 13, 1], 'representative': 39867867869, 'size': 144}
  • id: 110869596
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 15, 'group_counter': 3, 'group_order': 7200, 'label': '5D1', 'order': 5, 'powers': [16, 16, 1], 'representative': 110000104569, 'size': 144}
  • id: 110869597
    {'aut_label': '5C1', 'centralizer': '144.a1.a1', 'counter': 16, 'group_counter': 3, 'group_order': 7200, 'label': '5D2', 'order': 5, 'powers': [15, 15, 1], 'representative': 6318424932, 'size': 144}
  • id: 110869598
    {'aut_label': '6A', 'centralizer': '20.a1.a1', 'counter': 17, 'group_counter': 3, 'group_order': 7200, 'label': '6A', 'order': 6, 'powers': [4, 2, 17], 'representative': 73330086274, 'size': 20}
  • id: 110869599
    {'aut_label': '6A', 'centralizer': '20.a1.b1', 'counter': 18, 'group_counter': 3, 'group_order': 7200, 'label': '6B', 'order': 6, 'powers': [5, 2, 18], 'representative': 34190468800, 'size': 20}
  • id: 110869600
    {'aut_label': '6C', 'centralizer': '400.a1.a1', 'counter': 19, 'group_counter': 3, 'group_order': 7200, 'label': '6C', 'order': 6, 'powers': [6, 2, 19], 'representative': 103211561084, 'size': 400}
  • id: 110869602
    {'aut_label': '10A1', 'centralizer': '12.a1.b1', 'counter': 20, 'group_counter': 3, 'group_order': 7200, 'label': '10A1', 'order': 10, 'powers': [9, 21, 2], 'representative': 42890630012, 'size': 12}
  • id: 110869603
    {'aut_label': '10A1', 'centralizer': '12.a1.b1', 'counter': 21, 'group_counter': 3, 'group_order': 7200, 'label': '10A3', 'order': 10, 'powers': [10, 20, 2], 'representative': 6328127508, 'size': 12}
  • id: 110869604
    {'aut_label': '10A1', 'centralizer': '12.a1.a1', 'counter': 22, 'group_counter': 3, 'group_order': 7200, 'label': '10B1', 'order': 10, 'powers': [11, 23, 2], 'representative': 96465312600, 'size': 12}
  • id: 110869605
    {'aut_label': '10A1', 'centralizer': '12.a1.a1', 'counter': 23, 'group_counter': 3, 'group_order': 7200, 'label': '10B3', 'order': 10, 'powers': [12, 22, 2], 'representative': 32970162552, 'size': 12}
  • id: 110869606
    {'aut_label': '10C1', 'centralizer': '144.a1.a1', 'counter': 24, 'group_counter': 3, 'group_order': 7200, 'label': '10C1', 'order': 10, 'powers': [13, 25, 2], 'representative': 48229809199, 'size': 144}
  • id: 110869607
    {'aut_label': '10C1', 'centralizer': '144.a1.a1', 'counter': 25, 'group_counter': 3, 'group_order': 7200, 'label': '10C3', 'order': 10, 'powers': [14, 24, 2], 'representative': 59525594000, 'size': 144}
  • id: 110869608
    {'aut_label': '10C1', 'centralizer': '144.a1.a1', 'counter': 26, 'group_counter': 3, 'group_order': 7200, 'label': '10D1', 'order': 10, 'powers': [15, 27, 2], 'representative': 97851824505, 'size': 144}
  • id: 110869609
    {'aut_label': '10C1', 'centralizer': '144.a1.a1', 'counter': 27, 'group_counter': 3, 'group_order': 7200, 'label': '10D3', 'order': 10, 'powers': [16, 26, 2], 'representative': 48945614367, 'size': 144}
  • id: 110869610
    {'aut_label': '12A', 'centralizer': '600.c1.a1', 'counter': 28, 'group_counter': 3, 'group_order': 7200, 'label': '12A', 'order': 12, 'powers': [17, 7, 28], 'representative': 85556871739, 'size': 600}
  • id: 110869611
    {'aut_label': '12A', 'centralizer': '600.c1.b1', 'counter': 29, 'group_counter': 3, 'group_order': 7200, 'label': '12B', 'order': 12, 'powers': [18, 8, 29], 'representative': 124721806487, 'size': 600}
  • id: 110869613
    {'aut_label': '15A1', 'centralizer': '240.a1.b1', 'counter': 30, 'group_counter': 3, 'group_order': 7200, 'label': '15A1', 'order': 15, 'powers': [31, 10, 5], 'representative': 40847547225, 'size': 240}
  • id: 110869614
    {'aut_label': '15A1', 'centralizer': '240.a1.b1', 'counter': 31, 'group_counter': 3, 'group_order': 7200, 'label': '15A2', 'order': 15, 'powers': [30, 9, 5], 'representative': 1472808265, 'size': 240}
  • id: 110869615
    {'aut_label': '15A1', 'centralizer': '240.a1.a1', 'counter': 32, 'group_counter': 3, 'group_order': 7200, 'label': '15B1', 'order': 15, 'powers': [33, 11, 4], 'representative': 495735408, 'size': 240}
  • id: 110869616
    {'aut_label': '15A1', 'centralizer': '240.a1.a1', 'counter': 33, 'group_counter': 3, 'group_order': 7200, 'label': '15B2', 'order': 15, 'powers': [32, 12, 4], 'representative': 45515882380, 'size': 240}
  • id: 110869617
    {'aut_label': '20A1', 'centralizer': '360.c1.a1', 'counter': 34, 'group_counter': 3, 'group_order': 7200, 'label': '20A1', 'order': 20, 'powers': [20, 35, 7], 'representative': 12363298319, 'size': 360}
  • id: 110869618
    {'aut_label': '20A1', 'centralizer': '360.c1.a1', 'counter': 35, 'group_counter': 3, 'group_order': 7200, 'label': '20A3', 'order': 20, 'powers': [21, 34, 7], 'representative': 55010046532, 'size': 360}
  • id: 110869619
    {'aut_label': '20A1', 'centralizer': '360.c1.b1', 'counter': 36, 'group_counter': 3, 'group_order': 7200, 'label': '20B1', 'order': 20, 'powers': [23, 37, 8], 'representative': 150645890675, 'size': 360}
  • id: 110869620
    {'aut_label': '20A1', 'centralizer': '360.c1.b1', 'counter': 37, 'group_counter': 3, 'group_order': 7200, 'label': '20B3', 'order': 20, 'powers': [22, 36, 8], 'representative': 75469528851, 'size': 360}
  • id: 110869621
    {'aut_label': '30A1', 'centralizer': '240.a1.b1', 'counter': 38, 'group_counter': 3, 'group_order': 7200, 'label': '30A1', 'order': 30, 'powers': [30, 21, 18], 'representative': 252408292, 'size': 240}
  • id: 110869622
    {'aut_label': '30A1', 'centralizer': '240.a1.b1', 'counter': 39, 'group_counter': 3, 'group_order': 7200, 'label': '30A7', 'order': 30, 'powers': [31, 20, 18], 'representative': 4158107233, 'size': 240}
  • id: 110869624
    {'aut_label': '30A1', 'centralizer': '240.a1.a1', 'counter': 40, 'group_counter': 3, 'group_order': 7200, 'label': '30B1', 'order': 30, 'powers': [32, 22, 17], 'representative': 100398701760, 'size': 240}
  • id: 110869625
    {'aut_label': '30A1', 'centralizer': '240.a1.a1', 'counter': 41, 'group_counter': 3, 'group_order': 7200, 'label': '30B7', 'order': 30, 'powers': [33, 23, 17], 'representative': 5377069755, 'size': 240}
• 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: 4770398
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.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], 'schur_index': 1}
  • id: 4770419
    {'cdim': 4, 'counter': 4, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.4a', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 0, 1, 4, 1, 4, 0, -1, -1, 4, 4, -1, -1, -1, -1, 1, 4, 1, -1, -1, 4, 4, -1, -1, -1, -1, 1, 0, 1, -1, -1, 1, -1, -1, 0, 0, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4770420
    {'cdim': 4, 'counter': 5, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.4b', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 1, 1, 0, 4, 4, 4, -1, -1, -1, -1, -1, -1, 4, 1, 1, 4, 4, -1, -1, -1, -1, -1, -1, 0, 1, -1, 1, 1, -1, 0, 0, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4770423
    {'cdim': 5, 'counter': 8, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.5a', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 1, -1, 5, -1, 5, 1, 0, 0, 5, 5, 0, 0, 0, 0, -1, 5, -1, 0, 0, 5, 5, 0, 0, 0, 0, -1, 1, -1, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4770424
    {'cdim': 5, 'counter': 9, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.5b', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 1, 5, -1, -1, 1, 5, 5, 5, 0, 0, 0, 0, 0, 0, 5, -1, -1, 5, 5, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, -1, 0, 1, 1, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4770409
    {'cdim': 3, 'counter': 2, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.3a', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, -2, 0, 6, 0, 6, -2, 1, 1, 6, 6, 1, 1, 1, 1, 0, 6, 0, 1, 1, 6, 6, 1, 1, 1, 1, 0, -2, 0, 1, 1, 0, 1, 1, -2, -2, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4770418
    {'cdim': 3, 'counter': 3, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.3b', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, -2, 6, 0, 0, -2, 6, 6, 6, 1, 1, 1, 1, 1, 1, 6, 0, 0, 6, 6, 1, 1, 1, 1, 1, 1, -2, 0, 1, 0, 0, 1, -2, -2, 1, 1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4770421
    {'cdim': 4, 'counter': 6, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.4c', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, 0, -4, -4, 2, 0, 0, -2, -2, -2, -2, -2, 3, 3, -2, 4, 4, -2, 2, 2, 2, 2, 2, -3, -3, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4770422
    {'cdim': 4, 'counter': 7, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.4d', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, 0, -4, -4, 2, 0, 0, -2, -2, -2, -2, 3, -2, -2, 3, 4, 4, -2, 2, 2, 2, 2, -3, 2, 2, -3, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4770399
    {'cdim': 8, 'counter': 10, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.8a', 'multiplicity': 2, 'nt': [720, 0], 'qdim': 16, 'qvalues': [16, -16, 0, -8, 4, -2, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, 8, -4, 2, 4, 4, 4, 4, -1, -1, -1, -1, 0, 0, 2, -1, -1, 2, 0, 0, 0, 0, 1, 1, -2, -2], 'schur_index': 1}
  • id: 4770400
    {'cdim': 8, 'counter': 11, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.8b', 'multiplicity': 2, 'nt': [720, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 4, -8, -2, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, -4, 8, 2, 4, 4, 4, 4, -1, -1, -1, -1, 0, 0, -1, 2, 2, -1, 0, 0, 0, 0, -2, -2, 1, 1], 'schur_index': 1}
  • id: 4770410
    {'cdim': 16, 'counter': 20, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.16a', 'multiplicity': 1, 'nt': [25, 77], 'qdim': 16, 'qvalues': [16, 16, 0, 4, 4, 1, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, 4, 4, 1, -4, -4, -4, -4, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4770411
    {'cdim': 16, 'counter': 21, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.16b', 'multiplicity': 1, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 4, 4, 1, 0, 0, -4, -4, -4, -4, 1, 1, 1, 1, -4, -4, -1, 4, 4, 4, 4, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4770401
    {'cdim': 9, 'counter': 12, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.9a', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 18, 2, 0, 0, 0, -6, -6, 3, 3, 3, 3, -2, 3, 3, -2, 0, 0, 0, 3, 3, 3, 3, -2, 3, 3, -2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4770402
    {'cdim': 9, 'counter': 13, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.9b', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 18, 'qvalues': [18, 18, 2, 0, 0, 0, -6, -6, 3, 3, 3, 3, 3, -2, -2, 3, 0, 0, 0, 3, 3, 3, 3, 3, -2, -2, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4770412
    {'cdim': 20, 'counter': 22, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.20a', 'multiplicity': 1, 'nt': [30, 472], 'qdim': 20, 'qvalues': [20, 20, 0, -4, 5, -1, 0, 4, 0, 0, -5, -5, 0, 0, 0, 0, -4, 5, -1, 0, 0, -5, -5, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, -1, -1, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4770413
    {'cdim': 20, 'counter': 23, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.20b', 'multiplicity': 1, 'nt': [30, 472], 'qdim': 20, 'qvalues': [20, 20, 0, 5, -4, -1, 4, 0, -5, -5, 0, 0, 0, 0, 0, 0, 5, -4, -1, -5, -5, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, -1, -1, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4770403
    {'cdim': 12, 'counter': 14, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.12a', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 6, 0, 0, -8, 4, 4, -6, -6, -1, -1, -1, -1, 0, 6, 0, 4, 4, -6, -6, -1, -1, -1, -1, 0, -2, 0, 1, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4770404
    {'cdim': 12, 'counter': 15, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.12b', 'multiplicity': 2, 'nt': [60, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 6, 0, 0, -8, 0, -6, -6, 4, 4, -1, -1, -1, -1, 6, 0, 0, -6, -6, 4, 4, -1, -1, -1, -1, -2, 0, 1, 0, 0, 1, 2, 2, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4770405
    {'cdim': 12, 'counter': 16, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.12c', 'multiplicity': 2, 'nt': [600, 0], 'qdim': 24, 'qvalues': [24, -24, 0, -12, 0, 0, 0, 0, -6, -6, 4, 4, -1, -1, -1, -1, 12, 0, 0, 6, 6, -4, -4, 1, 1, 1, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2], 'schur_index': 1}
  • id: 4770406
    {'cdim': 12, 'counter': 17, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.12d', 'multiplicity': 2, 'nt': [600, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, -12, 0, 0, 0, 4, 4, -6, -6, -1, -1, -1, -1, 0, 12, 0, -4, -4, 6, 6, 1, 1, 1, 1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0], 'schur_index': 1}
  • id: 4770414
    {'cdim': 24, 'counter': 24, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.24a', 'multiplicity': 1, 'nt': [240, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 6, 0, 0, 0, 4, 4, -6, -6, -1, -1, -1, -1, 0, -6, 0, -4, -4, 6, 6, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0], 'schur_index': 2}
  • id: 4770415
    {'cdim': 24, 'counter': 25, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.24b', 'multiplicity': 1, 'nt': [240, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 6, 0, 0, 0, 0, -6, -6, 4, 4, -1, -1, -1, -1, -6, 0, 0, 6, 6, -4, -4, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 2}
  • id: 4770416
    {'cdim': 25, 'counter': 26, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.25a', 'multiplicity': 1, 'nt': [36, 4580], 'qdim': 25, 'qvalues': [25, 25, 1, -5, -5, 1, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4770407
    {'cdim': 15, 'counter': 18, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.15a', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 30, 'qvalues': [30, 30, -2, -6, 0, 0, -10, 6, 0, 0, 5, 5, 0, 0, 0, 0, -6, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4770408
    {'cdim': 15, 'counter': 19, 'faithful': False, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.15b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 30, 'qvalues': [30, 30, -2, 0, -6, 0, 6, -10, 5, 5, 0, 0, 0, 0, 0, 0, 0, -6, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0, 1, 1, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4770417
    {'cdim': 36, 'counter': 27, 'faithful': True, 'group': '7200.c', 'group_order': 7200, 'image': None, 'label': '7200.c.36a', 'multiplicity': 1, 'nt': [120, 0], 'qdim': 36, 'qvalues': [36, -36, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 1, 1, 1, 1, 0, 0, 0, -6, -6, -6, -6, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 7776553
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 7200, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 7200, 'label': '7200.c.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]]]}
  • id: 7776564
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 120, 'counter': 2, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 120, 'label': '7200.c.3a1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-1, 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]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[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]]]}
  • id: 7776575
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 120, 'counter': 3, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 120, 'label': '7200.c.3a2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-1, 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]], [[0, 0]], [[3, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[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]]]}
  • id: 7776586
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 120, 'counter': 4, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 120, 'label': '7200.c.3b1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[3, 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, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 7776589
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 120, 'counter': 5, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 120, 'label': '7200.c.3b2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[3, 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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 7776590
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 120, 'counter': 6, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 120, 'label': '7200.c.4a', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7776591
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 120, 'counter': 7, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 120, 'label': '7200.c.4b', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 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: 7776592
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 8, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.4c1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 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]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 7776593
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 9, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.4c2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 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]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 7776554
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 10, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.4d1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 7776555
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 11, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.4d2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 7776556
    {'center': '60.a1.b1', 'center_index': 60, 'center_order': 120, 'counter': 12, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 120, 'label': '7200.c.5a', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7776557
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 120, 'counter': 13, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 120, 'label': '7200.c.5b', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[5, 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]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7776558
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 14, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.8a1', 'nt': [720, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 7776559
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 15, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.8a2', 'nt': [720, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]]]}
  • id: 7776560
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 16, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.8b1', 'nt': [720, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 2], [4, -2]], [[4, 1], [4, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-2, 0]], [[4, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 7776561
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 17, 'cyclotomic_n': 5, 'dim': 8, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.8b2', 'nt': [720, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 1], [4, -1]], [[4, 2], [4, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[4, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 7776562
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 18, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.9a1', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[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: 7776563
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 19, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.9a2', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 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]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[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: 7776565
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 20, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.9b1', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 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: 7776566
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 21, 'cyclotomic_n': 5, 'dim': 9, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.9b2', 'nt': [60, 0], 'q_character': None, 'values': [[[9, 0]], [[9, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 2], [-3, -2]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 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: 7776567
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 22, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.12a1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[0, 0]], [[3, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[-3, 0]], [[-3, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]]]}
  • id: 7776568
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.12a2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[0, 0]], [[3, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[-3, 0]], [[-3, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 7776569
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 24, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.12b1', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 1], [-4, -1]], [[-4, 2], [-4, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[3, 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, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 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]]]}
  • id: 7776570
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 25, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.12b2', 'nt': [60, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-4, 2], [-4, -2]], [[-4, 1], [-4, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[3, 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, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 7776571
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 26, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.12c1', 'nt': [600, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 2], [6, -2]], [[6, 1], [6, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7776572
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.12c2', 'nt': [600, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [6, -1]], [[6, 2], [6, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7776573
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.12d1', 'nt': [600, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[6, 2], [6, -2]], [[6, 1], [6, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-6, 1], [-6, -1]], [[-6, 2], [-6, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7776574
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.12d2', 'nt': [600, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[6, 1], [6, -1]], [[6, 2], [6, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-6, 2], [-6, -2]], [[-6, 1], [-6, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7776576
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.15a1', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 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]], [[1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 7776577
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.15a2', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 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]], [[1, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 7776578
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.15b1', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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]]]}
  • id: 7776579
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 33, 'cyclotomic_n': 5, 'dim': 15, 'faithful': False, 'field': [-1, -1, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.15b2', 'nt': [72, 0], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-5, 0]], [[-5, 2], [-5, -2]], [[-5, 1], [-5, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-5, 1], [-5, -1]], [[-5, 2], [-5, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[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]]]}
  • id: 7776580
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.16a', 'nt': [25, 77], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7776581
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.16b', 'nt': [120, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7776582
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 36, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.20a', 'nt': [30, 472], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[0, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[5, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7776583
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 37, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.20b', 'nt': [30, 472], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[0, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[5, 0]], [[-4, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7776584
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 38, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.24a', 'nt': [240, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7776585
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 39, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.24b', 'nt': [240, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7776587
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 1, 'dim': 25, 'faithful': False, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '3600.a', 'image_order': 3600, 'indicator': 1, 'kernel': '3600.a1.a1', 'kernel_order': 2, 'label': '7200.c.25a', 'nt': [36, 4580], 'q_character': None, 'values': [[[25, 0]], [[25, 0]], [[1, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[5, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7776588
    {'center': '3600.a1.a1', 'center_index': 3600, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 1, 'dim': 36, 'faithful': True, 'field': [0, 1], 'group': '7200.c', 'group_counter': 3, 'group_order': 7200, 'image': None, 'image_isoclass': '7200.c', 'image_order': 7200, 'indicator': 1, 'kernel': '7200.a1.a1', 'kernel_order': 1, 'label': '7200.c.36a', 'nt': [120, 0], 'q_character': None, 'values': [[[36, 0]], [[-36, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 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]]]}
• 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: 68225676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 7200, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '7200.c.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': True, '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': ['D', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7200.c', 'subgroup_hash': 5216169401806534062, 'subgroup_order': 7200, 'subgroup_tex': '\\OmegaPlus(4,5)', 'supersolvable': False, 'sylow': 0}
  • id: 68225738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '1440.4615', 'subgroup_hash': 4615, 'subgroup_order': 1440, 'subgroup_tex': '\\SL(2,5):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '1440.4615', 'subgroup_hash': 4615, 'subgroup_order': 1440, 'subgroup_tex': '\\SL(2,5):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.6.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '1200.481', 'subgroup_hash': 481, 'subgroup_order': 1200, 'subgroup_tex': '\\SL(2,5):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 68225771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.6.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '1200.481', 'subgroup_hash': 481, 'subgroup_order': 1200, 'subgroup_tex': '\\SL(2,5):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 68225782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '720.418', 'subgroup_hash': 418, 'subgroup_order': 720, 'subgroup_tex': '\\SL(2,5):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68225793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '720.418', 'subgroup_hash': 418, 'subgroup_order': 720, 'subgroup_tex': '\\SL(2,5):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68225804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 120, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '600.54', 'subgroup_hash': 54, 'subgroup_order': 600, 'subgroup_tex': 'C_5\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 68225815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 120, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '600.54', 'subgroup_hash': 54, 'subgroup_order': 600, 'subgroup_tex': 'C_5\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 68225677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '480.959', 'subgroup_hash': 959, 'subgroup_order': 480, 'subgroup_tex': '\\SL(2,5):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 68225688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 120, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '480.959', 'subgroup_hash': 959, 'subgroup_order': 480, 'subgroup_tex': '\\SL(2,5):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 68225699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 120, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '360.51', 'subgroup_hash': 51, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 68225710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 120, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '360.51', 'subgroup_hash': 51, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 68225721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '7200.c.25.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '288.860', 'subgroup_hash': 860, 'subgroup_order': 288, 'subgroup_tex': '\\OmegaPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.108', 'subgroup_hash': 108, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 68225734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.108', 'subgroup_hash': 108, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,3):D_5', 'supersolvable': False, 'sylow': 0}
  • id: 68225735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 120, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.93', 'subgroup_hash': 93, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,5):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 68225736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 120, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.93', 'subgroup_hash': 93, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,5):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 68225737
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.127', 'subgroup_hash': 127, 'subgroup_order': 144, 'subgroup_tex': '\\SL(2,3):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68225740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.50.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.127', 'subgroup_hash': 127, 'subgroup_order': 144, 'subgroup_tex': '\\SL(2,3):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68225741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': True, 'centralizer_order': 120, 'characteristic': False, 'core_order': 120, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '7200.c.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': True, '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': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 68225742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': True, 'centralizer_order': 120, 'characteristic': False, 'core_order': 120, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '7200.c.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': True, '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': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 68225743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.10', 'subgroup_hash': 10, 'subgroup_order': 120, 'subgroup_tex': 'D_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.60.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.10', 'subgroup_hash': 10, 'subgroup_order': 120, 'subgroup_tex': 'D_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.60.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, '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': 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: 68225746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.60.c1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, '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': 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: 68225747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '120.15', 'subgroup_hash': 15, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.60.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '120.15', 'subgroup_hash': 15, 'subgroup_order': 120, 'subgroup_tex': 'C_5\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.72.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.75.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 68225754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.75.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.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': 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': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 68225755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.75.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.75.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.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': 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': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68225758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.90.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68225759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.100.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.100.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.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': 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': '72.25', 'subgroup_hash': 25, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225763
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68225764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.120.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.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': 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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68225765
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225766
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.120.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225767
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225768
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.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': 120, '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: 68225770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.120.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.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': 120, '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: 68225772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.144.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b2.a1', 'outer_equivalence': False, 'perfect': False, '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': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.150.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 68225776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.150.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 68225777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.150.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68225778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.150.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68225779
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.180.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68225785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.180.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68225786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.200.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '200.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': 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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '7200.c.225.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 68225790
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68225791
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.240.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68225792
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68225794
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.240.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68225795
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.240.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68225796
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.240.b1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.b1.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': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68225797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 5, 'label': '7200.c.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': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
  • id: 68225798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.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': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68225806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68225807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.300.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 68225811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.360.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225816
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225817
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.360.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 68225818
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225819
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.400.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '400.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': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.450.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68225824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.450.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68225825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.450.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225678
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.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': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68225679
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.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': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68225680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225683
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.600.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225684
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.600.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68225685
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.600.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225686
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.600.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.600.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '600.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': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 68225690
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225691
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225692
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225693
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.720.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68225694
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225695
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225696
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.720.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225697
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.720.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225698
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.720.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.d2.a1', 'outer_equivalence': False, 'perfect': False, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225700
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.720.d2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.d2.b1', 'outer_equivalence': False, 'perfect': False, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '7200.c.800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 68225702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.900.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.900.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.900.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.900.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68225706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.900.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68225707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.900.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68225708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.900.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 68225709
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 2, 'counter': 129, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225711
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1200.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1200.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225712
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1200.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68225713
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.1200.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225714
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.1200.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225715
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.1200.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225716
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.1200.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1200.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68225717
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225718
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1440.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 68225719
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1440.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 68225720
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1440.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 68225722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68225723
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 141, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1800.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225724
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.1800.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68225725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.1800.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68225726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '7200.c.1800.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 68225727
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.2400.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 68225728
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.2400.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 68225729
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.2400.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 68225730
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': True, 'central_factor': False, 'centralizer_order': 7200, 'characteristic': True, 'core_order': 2, 'counter': 148, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '7200.c.3600.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'S', 'U0', 'C2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68225731
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '7200.c.3600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 68225733
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '7200.c', 'ambient_counter': 3, 'ambient_order': 7200, 'ambient_tex': '\\OmegaPlus(4,5)', 'central': True, 'central_factor': False, 'centralizer_order': 7200, 'characteristic': True, 'core_order': 1, 'counter': 150, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '7200.c.7200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '7200.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '7200.c', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5216169401806534062, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 7200, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\OmegaPlus(4,5)', 'simple': False, 'solvable': True, 'special_labels': ['U1', 'C3'], '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: 68225676
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': ['7200.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['5.a1.a1', '5.a1.b1', '6.a1.a1', '6.a1.b1', '10.a1.a1', '10.a1.b1', '60.c1.a1', '60.c1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2746, 5000, 7247, 6040, 4308, 5000, 6578, 5000], 'generators': [984438000, 1960527931, 122109387504], 'label': '7200.c.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['60.a1.a1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '3600.a', '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': '3600.a'}
  • id: 68225677
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1'], 'contains': ['30.b1.a1', '75.a1.a1', '90.a1.a1', '150.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5270, -1, 6705, -1, 4319, -1, 4294, -1], 'generators': [59466171661, 62276962503, 61054853203, 40900888562, 122109387504], 'label': '7200.c.15.a1.a1', '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.a1.a1', 'projective_image': '3600.a', '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: 68225678
    {'ambient': '7200.c', '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': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '240.b1.a1', '240.b1.a2'], 'contains': ['1440.a1.b1', '2400.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6357, -1, 3612, -1, 6721, -1, 1565, -1], 'generators': [67304696262, 1718498999], 'label': '7200.c.480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '480.a1.a1', 'projective_image': '7200.c', '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': '4.2'}
  • id: 68225679
    {'ambient': '7200.c', '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': '240.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.b1', '240.b1.b1', '240.b1.b2'], 'contains': ['1440.a1.a1', '2400.a1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6357, -1, 5535, -1, 6721, -1, 6945, -1], 'generators': [63497584402, 12324220642], 'label': '7200.c.480.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '480.a1.b1', 'projective_image': '7200.c', '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': '4.2'}
  • id: 68225680
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '200.a1.a1', '300.a1.a1', '300.c1.a1'], 'contains': ['1200.a1.a1', '1200.c1.a1', '1800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4909, -1, 4394, -1, 4809, -1, 4158, -1], 'generators': [34219934376, 73457039382, 122109387504], 'label': '7200.c.600.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '600.a1.a1', 'projective_image': '3600.a', '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: 68225681
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.b1', '200.a1.a1', '300.a1.b1', '300.c1.b1'], 'contains': ['1200.a1.b1', '1200.c1.b1', '1800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4909, -1, 6041, -1, 4809, -1, 6725, -1], 'generators': [96465400078, 78400291952, 122109387504], 'label': '7200.c.600.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.b1', 'old_label': '600.a1.b1', 'projective_image': '3600.a', '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: 68225682
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '60.c1.b1', '200.a1.a1'], 'contains': ['1200.b1.a1', '1200.d1.a1', '1200.d1.a2', '1800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [1008, -1, 2188, -1, 1558, -1, 8706, -1], 'generators': [102315991353, 151743167406, 122109387504], 'label': '7200.c.600.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.b1.a1', 'old_label': '600.b1.a1', 'projective_image': '3600.a', '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': '6.1'}
  • id: 68225683
    {'ambient': '7200.c', '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': '600.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '150.a1.a1', '200.b1.a1', '300.a1.a1', '300.c1.a1', '300.d1.a1'], 'contains': ['1200.a1.a1', '1800.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4108, -1, 7090, -1, 4368, -1, 3845, -1], 'generators': [24501953774, 63497275003, 122109387504], 'label': '7200.c.600.c1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '600.c1.a1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225684
    {'ambient': '7200.c', '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': '600.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.b1', '150.a1.b1', '200.b1.b1', '300.a1.b1', '300.c1.b1', '300.d1.b1'], 'contains': ['1200.a1.b1', '1800.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4108, -1, 8946, -1, 4368, -1, 5948, -1], 'generators': [4151760677, 109882823127, 122109387504], 'label': '7200.c.600.c1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.b1', 'old_label': '600.c1.b1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225685
    {'ambient': '7200.c', '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': '60.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '120.b1.a1', '200.b1.b1', '300.a1.a1'], 'contains': ['1200.a1.a1', '1800.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2681, -1, 7918, -1, 5116, -1, 3470, -1], 'generators': [91572275002, 73457039382, 122109387504], 'label': '7200.c.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': '3600.a', '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': '6.1'}
  • id: 68225686
    {'ambient': '7200.c', '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': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.b1', '120.b1.b1', '200.b1.a1', '300.a1.b1'], 'contains': ['1200.a1.b1', '1800.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2681, -1, 8545, -1, 5116, -1, 6374, -1], 'generators': [96465400078, 125772346976, 122109387504], 'label': '7200.c.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': '3600.a', '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': '6.1'}
  • id: 68225687
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '300.b1.a1'], 'contains': ['1800.c1.a1', '2400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [369, -1, 987, -1, 630, -1, 9376, -1], 'generators': [151622661879, 4645543588, 110078508623], 'label': '7200.c.600.e1.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.e1.a1', 'projective_image': '7200.c', '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': '12.3'}
  • id: 68225688
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.b1.b1', '75.a1.b1', '90.a1.b1', '150.b1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [5270, -1, 8376, -1, 4319, -1, 5130, -1], 'generators': [75469338802, 75469234400, 91767587507, 109882823127, 122109387504], 'label': '7200.c.15.a1.b1', '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.a1.b1', 'projective_image': '3600.a', '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: 68225689
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '300.b1.a2'], 'contains': ['1800.c1.a2', '2400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [369, -1, 726, -1, 630, -1, 9001, -1], 'generators': [151622661879, 5618498947, 30703372091], 'label': '7200.c.600.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a2', 'old_label': '600.e1.a2', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.e1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 68225690
    {'ambient': '7200.c', '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': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.a1.b1', '360.a1.a1', '360.c1.a1', '360.d1.b1'], 'contains': ['1440.a1.a1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8395, -1, 3097, -1, 6392, -1, 4323, -1], 'generators': [12324220642, 122109387504], 'label': '7200.c.720.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '720.a1.a1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225691
    {'ambient': '7200.c', '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': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '240.a1.a1', '360.a1.b1', '360.c1.b1', '360.d1.a1'], 'contains': ['1440.a1.b1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8395, -1, 3366, -1, 6392, -1, 2117, -1], 'generators': [2442743828, 122109387504], 'label': '7200.c.720.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '720.a1.b1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225692
    {'ambient': '7200.c', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '360.b1.a1'], 'contains': ['1440.b1.a1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7955, -1, 1279, -1, 7596, -1, 3103, -1], 'generators': [124606653149, 122109387504], 'label': '7200.c.720.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '720.b1.a1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225693
    {'ambient': '7200.c', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '360.b1.b1'], 'contains': ['1440.b1.b1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7955, -1, 2275, -1, 7596, -1, 2922, -1], 'generators': [123388293774, 122109387504], 'label': '7200.c.720.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '720.b1.b1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225694
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.b2.a1', '240.b1.b1', '240.b1.b2', '360.a1.a1'], 'contains': ['1440.a1.a1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [9013, -1, 1621, -1, 7297, -1, 4636, -1], 'generators': [6791032020, 12324220642], 'label': '7200.c.720.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '720.c1.a1', 'projective_image': '7200.c', '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': '10.1'}
  • id: 68225695
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.b2.a1', '240.b1.a1', '240.b1.a2', '360.a1.b1'], 'contains': ['1440.a1.b1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [9013, -1, 1748, -1, 7297, -1, 2436, -1], 'generators': [146494240029, 3663131302], 'label': '7200.c.720.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.b1', 'old_label': '720.c1.b1', 'projective_image': '7200.c', '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': '10.1'}
  • id: 68225696
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '144.b1.a1', '360.b1.a1'], 'contains': ['1440.b1.a1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7276, -1, 138, -1, 7028, -1, 3713, -1], 'generators': [34274621881, 34389456256], 'label': '7200.c.720.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '720.d1.a1', 'projective_image': '7200.c', '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': '10.1'}
  • id: 68225697
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '144.b1.a1', '360.b1.b1'], 'contains': ['1440.b1.b1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7276, -1, 570, -1, 7028, -1, 3565, -1], 'generators': [34274621881, 35607815631], 'label': '7200.c.720.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.b1', 'old_label': '720.d1.b1', 'projective_image': '7200.c', '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': '10.1'}
  • id: 68225698
    {'ambient': '7200.c', 'aut_centralizer_order': None, 'aut_label': '720.d2', '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.b2.a1', '360.b1.a1'], 'contains': ['1440.b1.a1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7669, -1, 309, -1, 7895, -1, 3416, -1], 'generators': [124721487524, 34389456256], 'label': '7200.c.720.d2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '720.d2.a1', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d2.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 68225699
    {'ambient': '7200.c', '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': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.a1.a1'], 'contains': ['60.a1.b1', '100.b1.a1', '120.c1.a1', '200.b1.a1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [3528, -1, 8930, -1, 4719, -1, 7472, -1], 'generators': [121711634187, 121711672400, 116093760018, 122109387504], 'label': '7200.c.20.a1.a1', '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.a1', 'projective_image': '3600.a', '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': '120.35'}
  • id: 68225700
    {'ambient': '7200.c', 'aut_centralizer_order': None, 'aut_label': '720.d2', '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.b2.a1', '360.b1.b1'], 'contains': ['1440.b1.b1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7669, -1, 704, -1, 7895, -1, 3268, -1], 'generators': [124721487524, 35607815631], 'label': '7200.c.720.d2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.b1', 'old_label': '720.d2.b1', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d2.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 68225701
    {'ambient': '7200.c', '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': '400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['400.a1.a1', '400.b1.a1', '400.b1.a2'], 'contains': ['2400.a1.a1', '2400.a1.b1', '2400.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [855, -1, 8293, -1, 2310, -1, 7676, -1], 'generators': [67304696262, 4645543588], 'label': '7200.c.800.a1.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': '800.a1.a1', 'projective_image': '7200.c', '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': '4.2'}
  • id: 68225702
    {'ambient': '7200.c', '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': '900.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.a1.b1', '300.a1.a1', '300.a1.b1', '450.a1.a1', '450.a1.b1', '450.b1.a1'], 'contains': ['1800.a1.a1', '1800.b1.a1', '1800.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [5699, -1, 6401, -1, 3949, -1, 4372, -1], 'generators': [63497275003, 109882823127, 122109387504], 'label': '7200.c.900.a1.a1', 'mobius_quo': None, 'mobius_sub': 16, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '900.a1.a1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225703
    {'ambient': '7200.c', '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': ['180.b1.a1', '300.c1.a1', '450.a1.b1', '450.b1.a1'], 'contains': ['1800.a1.a1', '1800.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [6071, -1, 4279, -1, 3552, -1, 5250, -1], 'generators': [63497275003, 146494333804, 122109387504], 'label': '7200.c.900.b1.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.b1.a1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225704
    {'ambient': '7200.c', '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': ['180.b1.b1', '300.c1.b1', '450.a1.a1', '450.b1.a1'], 'contains': ['1800.a1.a1', '1800.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [6071, -1, 6204, -1, 3552, -1, 4586, -1], 'generators': [31930090641, 109882823127, 122109387504], 'label': '7200.c.900.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': '900.b1.b1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225705
    {'ambient': '7200.c', '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': '900.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.b1.a1', '450.b1.a1'], 'contains': ['1800.a1.a1', '1800.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2002, -1, 3072, -1, 2699, -1, 8391, -1], 'generators': [31930090641, 146494333804, 122109387504], 'label': '7200.c.900.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a2', 'old_label': '900.c1.a1', 'projective_image': '3600.a', '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: 68225706
    {'ambient': '7200.c', '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': '900.c1.a2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.b1.a2', '450.b1.a1'], 'contains': ['1800.a1.a1', '1800.c1.a2'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [2002, -1, 2928, -1, 2699, -1, 7689, -1], 'generators': [76496885632, 146494333804, 122109387504], 'label': '7200.c.900.c1.a2', '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.c1.a2', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.c1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 68225707
    {'ambient': '7200.c', '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': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '300.d1.a1', '300.e1.b1', '300.f1.a1', '450.a1.b1'], 'contains': ['1800.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3919, -1, 6063, -1, 3268, -1, 5101, -1], 'generators': [91582350027, 63497275003, 122109387504], 'label': '7200.c.900.d1.a1', '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.d1.a1', 'projective_image': '3600.a', '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: 68225708
    {'ambient': '7200.c', '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': '60.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.b1', '300.d1.b1', '300.e1.a1', '300.f1.b1', '450.a1.a1'], 'contains': ['1800.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3919, -1, 7684, -1, 3268, -1, 4010, -1], 'generators': [91767587507, 109882823127, 122109387504], 'label': '7200.c.900.d1.b1', '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.d1.b1', 'projective_image': '3600.a', '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: 68225709
    {'ambient': '7200.c', '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': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '300.e1.a1', '400.a1.a1', '600.a1.a1', '600.c1.a1', '600.d1.a1'], 'contains': ['2400.a1.a1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3225, -1, 7951, -1, 4723, -1, 3861, -1], 'generators': [24501953774, 122109387504], 'label': '7200.c.1200.a1.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.a1.a1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225710
    {'ambient': '7200.c', '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': '1200.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1', '10.a1.b1'], 'contains': ['60.a1.a1', '100.b1.b1', '120.c1.b1', '200.b1.b1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3528, -1, 9502, -1, 4719, -1, 6566, -1], 'generators': [32970078200, 150803406775, 55068363144, 122109387504], 'label': '7200.c.20.a1.b1', '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.b1', 'projective_image': '3600.a', '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': '120.35'}
  • id: 68225711
    {'ambient': '7200.c', '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': '20.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.b1', '300.e1.b1', '400.a1.a1', '600.a1.b1', '600.c1.b1', '600.d1.b1'], 'contains': ['2400.a1.b1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3225, -1, 8464, -1, 4723, -1, 6467, -1], 'generators': [1222581276, 122109387504], 'label': '7200.c.1200.a1.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.a1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68225712
    {'ambient': '7200.c', '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': '400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.b1.a1', '300.b1.a2', '300.f1.a1', '300.f1.b1', '400.a1.a1', '600.b1.a1'], 'contains': ['2400.b1.a1', '3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [1319, -1, 2650, -1, 1592, -1, 8072, -1], 'generators': [4645543588, 122109387504], 'label': '7200.c.1200.b1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.a1.a1', 'old_label': '1200.b1.a1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225713
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '240.b1.a2', '400.b1.a1', '400.b1.a2', '600.a1.a1'], 'contains': ['2400.a1.a1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4773, -1, 4460, -1, 4993, -1, 4158, -1], 'generators': [34219934376, 73457039382], 'label': '7200.c.1200.c1.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': '1200.c1.a1', 'projective_image': '7200.c', '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': '6.1'}
  • id: 68225714
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.b1', '240.b1.b2', '400.b1.a1', '400.b1.a2', '600.a1.b1'], 'contains': ['2400.a1.b1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [4773, -1, 5199, -1, 4993, -1, 7328, -1], 'generators': [62277193802, 78400291952], 'label': '7200.c.1200.c1.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': '1200.c1.b1', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68225715
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '400.b1.a2', '600.b1.a1'], 'contains': ['2400.b1.a1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [97, -1, 913, -1, 1895, -1, 8706, -1], 'generators': [102315991353, 151743167406], 'label': '7200.c.1200.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.b1.a1', 'old_label': '1200.d1.a1', 'projective_image': '7200.c', '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': '6.1'}
  • id: 68225716
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.b1', '400.b1.a1', '600.b1.a1'], 'contains': ['2400.b1.a1', '3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 600, 'diagramx': [97, -1, 1242, -1, 1895, -1, 8389, -1], 'generators': [88164965027, 151743167406], 'label': '7200.c.1200.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '600.b1.a1', 'old_label': '1200.d1.a2', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1200.d1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68225717
    {'ambient': '7200.c', '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': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '480.a1.b1', '720.a1.a1', '720.c1.a1'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8924, -1, 1792, -1, 6721, -1, 4364, -1], 'generators': [12324220642], 'label': '7200.c.1440.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '1440.a1.a1', 'projective_image': '7200.c', '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': '2.1'}
  • id: 68225718
    {'ambient': '7200.c', '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': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '480.a1.a1', '720.a1.b1', '720.c1.b1'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8924, -1, 1920, -1, 6721, -1, 2436, -1], 'generators': [3663131302], 'label': '7200.c.1440.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '1440.a1.b1', 'projective_image': '7200.c', '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': '2.1'}
  • id: 68225719
    {'ambient': '7200.c', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '720.b1.a1', '720.d1.a1', '720.d2.a1'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7683, -1, 204, -1, 7596, -1, 3416, -1], 'generators': [34389456256], 'label': '7200.c.1440.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '1440.b1.a1', 'projective_image': '7200.c', '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': '2.1'}
  • id: 68225720
    {'ambient': '7200.c', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '720.b1.b1', '720.d1.b1', '720.d2.b1'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7683, -1, 540, -1, 7596, -1, 3268, -1], 'generators': [35607815631], 'label': '7200.c.1440.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '1440.b1.b1', 'projective_image': '7200.c', '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': '2.1'}
  • id: 68225721
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.a1.b1'], 'contains': ['75.a1.a1', '75.a1.b1', '75.b1.a1', '75.b1.a2', '100.b1.a1', '100.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3536, -1, 7915, -1, 3100, -1, 7573, -1], 'generators': [49033514824, 24501953774, 4645543588, 63497275003, 91767587507, 109882823127, 122109387504], 'label': '7200.c.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': '3600.a', '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': '144.184'}
  • id: 68225722
    {'ambient': '7200.c', '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': '450.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.a1.b1', '360.b1.a1', '360.b1.b1', '600.a1.a1', '600.a1.b1', '600.b1.a1', '900.a1.a1', '900.b1.a1', '900.b1.b1', '900.c1.a1', '900.c1.a2'], 'contains': ['3600.a1.a1', '3600.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [5531, -1, 3140, -1, 4166, -1, 4794, -1], 'generators': [38857825626, 122109387504], 'label': '7200.c.1800.a1.a1', 'mobius_quo': None, 'mobius_sub': -32, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '225.a1.a1', 'old_label': '1800.a1.a1', 'projective_image': '3600.a', '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: 68225723
    {'ambient': '7200.c', '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': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.a1', '360.d1.a1', '600.c1.a1', '600.d1.b1', '900.a1.a1', '900.b1.a1', '900.d1.a1'], 'contains': ['3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6307, -1, 5744, -1, 4454, -1, 4488, -1], 'generators': [63497275003, 122109387504], 'label': '7200.c.1800.b1.a1', 'mobius_quo': None, 'mobius_sub': -240, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '1800.b1.a1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225724
    {'ambient': '7200.c', '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': '30.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.b1', '360.d1.b1', '600.c1.b1', '600.d1.a1', '900.a1.a1', '900.b1.b1', '900.d1.b1'], 'contains': ['3600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6307, -1, 6928, -1, 4454, -1, 4010, -1], 'generators': [109882823127, 122109387504], 'label': '7200.c.1800.b1.b1', 'mobius_quo': None, 'mobius_sub': -240, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '1800.b1.b1', 'projective_image': '3600.a', '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': '2.1'}
  • id: 68225725
    {'ambient': '7200.c', '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': '900.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.e1.a1', '900.c1.a1'], 'contains': ['3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [855, -1, 1724, -1, 2699, -1, 8548, -1], 'generators': [31930090641, 146494333804], 'label': '7200.c.1800.c1.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': '1800.c1.a1', 'projective_image': '7200.c', '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': '3.1'}
  • id: 68225726
    {'ambient': '7200.c', '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': '900.c1.a2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.e1.a2', '900.c1.a2'], 'contains': ['3600.b1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [855, -1, 1579, -1, 2699, -1, 8230, -1], 'generators': [76496885632, 146494333804], 'label': '7200.c.1800.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a2', 'old_label': '1800.c1.a2', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.c1.a2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 68225727
    {'ambient': '7200.c', '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': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.a1', '800.a1.a1', '1200.a1.a1', '1200.c1.a1'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4773, -1, 8074, -1, 4858, -1, 4067, -1], 'generators': [24501953774], 'label': '7200.c.2400.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '2400.a1.a1', 'projective_image': '7200.c', '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': '2.1'}
  • id: 68225728
    {'ambient': '7200.c', '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': '20.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.b1', '800.a1.a1', '1200.a1.b1', '1200.c1.b1'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4773, -1, 8205, -1, 4858, -1, 6945, -1], 'generators': [4883293854], 'label': '7200.c.2400.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.b1', 'old_label': '2400.a1.b1', 'projective_image': '7200.c', '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': '2.1'}
  • id: 68225729
    {'ambient': '7200.c', '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': '400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['600.e1.a1', '600.e1.a2', '800.a1.a1', '1200.b1.a1', '1200.d1.a1', '1200.d1.a2'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [504, -1, 1086, -1, 1895, -1, 8389, -1], 'generators': [4645543588], 'label': '7200.c.2400.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '200.a1.a1', 'old_label': '2400.b1.a1', 'projective_image': '7200.c', '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': '2.1'}
  • id: 68225730
    {'ambient': '7200.c', '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': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '720.a1.b1', '720.b1.a1', '720.b1.b1', '1200.a1.a1', '1200.a1.b1', '1200.b1.a1', '1800.a1.a1', '1800.b1.a1', '1800.b1.b1'], 'contains': ['7200.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7140, 5000, 3313, 4999, 4589, 5000, 4216, 5000], 'generators': [122109387504], 'label': '7200.c.3600.a1.a1', 'mobius_quo': -1, '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': '3600.a', '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': '1.1'}
  • id: 68225731
    {'ambient': '7200.c', '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': '450.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.c1.a1', '720.c1.b1', '720.d1.a1', '720.d1.b1', '720.d2.a1', '720.d2.b1', '1200.c1.a1', '1200.c1.b1', '1200.d1.a1', '1200.d1.a2', '1800.a1.a1', '1800.c1.a1', '1800.c1.a2'], 'contains': ['7200.a1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 450, 'diagramx': [5771, -1, 1405, -1, 5127, -1, 4595, -1], 'generators': [38857825626], 'label': '7200.c.3600.b1.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.b1.a1', 'projective_image': '7200.c', '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': '1.1'}
  • id: 68225732
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '6.a1.a1'], 'contains': ['60.d1.a1', '90.a1.b1', '120.c1.a1', '150.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5696, -1, 7440, -1, 5823, -1, 2251, -1], 'generators': [24501953774, 5617926781, 91767587507, 91582193827, 109882823127, 122109387504], 'label': '7200.c.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': '3600.a', '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': '120.39'}
  • id: 68225733
    {'ambient': '7200.c', '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': '1.a1.a1', 'complements': ['1.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.b1.a1'], 'contains': [], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6682, 5000, 1815, 4999, 4993, 5000, 4216, 5000], 'generators': [], 'label': '7200.c.7200.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '7200.a1.a1', 'normal_contained_in': ['3600.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '7200.a1.a1', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68225734
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1', '6.a1.b1'], 'contains': ['60.d1.b1', '90.a1.a1', '120.c1.b1', '150.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5696, -1, 5482, -1, 5823, -1, 5911, -1], 'generators': [62276962503, 63497584402, 122109387504, 61054853203, 6791032020, 6162126234], 'label': '7200.c.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': '3600.a', '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': '120.39'}
  • id: 68225735
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.b1', '15.a1.a1'], 'contains': ['60.a1.a1', '150.a1.a1', '180.a1.a1', '300.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4601, -1, 6834, -1, 5427, -1, 3359, -1], 'generators': [81039464397, 62276962503, 115085164381, 122109387504], 'label': '7200.c.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '3600.a', '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': '120.35'}
  • id: 68225736
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '10.a1.a1', '15.a1.b1'], 'contains': ['60.a1.b1', '150.a1.b1', '180.a1.b1', '300.a1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [4601, -1, 8644, -1, 5427, -1, 5264, -1], 'generators': [75469338802, 75469234400, 109882823127, 122109387504], 'label': '7200.c.30.b1.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '30.b1.b1', 'projective_image': '3600.a', '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': '120.35'}
  • id: 68225737
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.a1.b1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.b1.b1', '180.a1.a1', '180.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8802, -1, 4127, -1, 8898, -1, 2537, -1], 'generators': [34274621881, 35410550001, 122158215649, 65937900003, 122109387504], 'label': '7200.c.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '3600.a', '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': '100.13'}
  • id: 68225738
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['15.a1.b1', '20.a1.a1', '25.a1.a1', '30.a1.a1', '50.a1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [4212, -1, 8182, -1, 4166, -1, 6648, -1], 'generators': [121711634187, 24501953774, 121711672400, 91767587507, 109882823127, 122109387504], 'label': '7200.c.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': '3600.a', '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': '720.768'}
  • id: 68225739
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.b1', '10.a1.a1'], 'contains': ['100.b1.a1', '150.a1.b1', '150.b1.a1', '200.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [2521, -1, 8172, -1, 3922, -1, 6230, -1], 'generators': [34219934376, 63497584402, 150823151748, 62276962503, 61054853203, 122109387504], 'label': '7200.c.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': '3600.a', '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': '72.44'}
  • id: 68225740
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.a1.b1'], 'contains': ['100.b1.b1', '150.a1.a1', '150.b1.b1', '200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [2521, -1, 9520, -1, 3922, -1, 6902, -1], 'generators': [24501953774, 52944489281, 91767587507, 109882823127, 125772346976, 122109387504], 'label': '7200.c.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': '3600.a', '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': '72.44'}
  • id: 68225741
    {'ambient': '7200.c', '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': '60.a1.b1', 'complements': ['120.d1.a1', '120.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.b1', '30.b1.a1'], 'contains': ['300.e1.a1', '360.d1.b1', '600.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4144, 5000, 7923, 7793, 5251, 5000, 2912, 7792], 'generators': [36748052518, 55068363144, 122109387504], 'label': '7200.c.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['3600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '3600.a', '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': '60.5'}
  • id: 68225742
    {'ambient': '7200.c', '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': '60.a1.a1', 'complements': ['120.d1.a1', '120.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.a1.a1', '30.b1.b1'], 'contains': ['300.e1.b1', '360.d1.a1', '600.d1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4144, 5000, 8746, 2207, 5251, 5000, 5592, 2208], 'generators': [124552268776, 124552109450, 122109387504], 'label': '7200.c.60.a1.b1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['3600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.b1', 'projective_image': '3600.a', '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': '60.5'}
  • id: 68225743
    {'ambient': '7200.c', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.c1.a1', '180.a1.b1', '300.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5949, -1, 4699, -1, 7368, -1, 994, -1], 'generators': [35410550001, 52774623751, 69012510019, 65937900003, 122109387504], 'label': '7200.c.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '60.b1.a1', 'projective_image': '3600.a', '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': '60.8'}
  • id: 68225744
    {'ambient': '7200.c', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '10.a1.b1'], 'contains': ['120.a1.b1', '120.b1.b1', '120.c1.b1', '180.a1.a1', '300.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5949, -1, 5414, -1, 7368, -1, 6471, -1], 'generators': [85498053770, 24861375880, 140439466896, 18951236390, 122109387504], 'label': '7200.c.60.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '60.b1.b1', 'projective_image': '3600.a', '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': '60.8'}
  • id: 68225745
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['120.d1.a1', '300.b1.a1', '360.b1.a1', '600.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1351, -1, 1284, -1, 814, -1, 9425, -1], 'generators': [97773444388, 12596547050, 122109387504], 'label': '7200.c.60.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.a1', 'old_label': '60.c1.a1', 'projective_image': '3600.a', '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': '60.5'}
  • id: 68225746
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['120.d1.b1', '300.b1.a2', '360.b1.b1', '600.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [1351, -1, 1586, -1, 814, -1, 9147, -1], 'generators': [19203562850, 3667344050, 122109387504], 'label': '7200.c.60.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.b1', 'old_label': '60.c1.b1', 'projective_image': '3600.a', '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': '60.5'}
  • id: 68225747
    {'ambient': '7200.c', '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': '720.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '30.a1.a1'], 'contains': ['180.c1.b1', '240.a1.a1', '300.e1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6811, -1, 7595, -1, 6754, -1, 1804, -1], 'generators': [24501953774, 5617926781, 91767587507, 109882823127, 122109387504], 'label': '7200.c.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225748
    {'ambient': '7200.c', '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': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '30.a1.b1'], 'contains': ['180.c1.a1', '240.a1.b1', '300.e1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6811, -1, 4989, -1, 6754, -1, 5975, -1], 'generators': [63497584402, 6162126234, 62276962503, 61054853203, 122109387504], 'label': '7200.c.60.d1.b1', '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.d1.b1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225749
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['15.a1.a1', '20.a1.b1', '25.a1.a1', '30.a1.b1', '50.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4212, -1, 7629, -1, 4166, -1, 6407, -1], 'generators': [63497584402, 59466171661, 150803406775, 62276962503, 61054853203, 122109387504], 'label': '7200.c.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': '3600.a', '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': '720.768'}
  • id: 68225750
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.b2.a1', '360.a1.a1', '360.a1.b1', '360.b1.a1', '360.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8570, -1, 1865, -1, 9721, -1, 2537, -1], 'generators': [34274621881, 35410550001, 122158215649, 122109387504], 'label': '7200.c.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '3600.a', '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': '100.13'}
  • id: 68225751
    {'ambient': '7200.c', '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': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '36.a1.a1'], 'contains': ['144.a1.a1', '360.c1.a1', '360.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9321, -1, 3544, -1, 9097, -1, 2117, -1], 'generators': [35410550001, 122158215649, 65937900003, 122109387504], 'label': '7200.c.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 68225752
    {'ambient': '7200.c', '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': '720.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '36.a1.a1'], 'contains': ['144.a1.a1', '360.c1.b1', '360.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9321, -1, 5608, -1, 9097, -1, 1490, -1], 'generators': [35410550001, 64831256268, 122158215649, 122109387504], 'label': '7200.c.72.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.b1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 68225753
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '25.a1.a1'], 'contains': ['150.a1.a1', '225.a1.a1', '300.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [4233, -1, 6993, -1, 3219, -1, 4160, -1], 'generators': [49033514824, 24501953774, 63497275003, 91767587507, 109882823127, 122109387504], 'label': '7200.c.75.a1.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.a1.a1', 'projective_image': '3600.a', '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: 68225754
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '25.a1.a1'], 'contains': ['150.a1.b1', '225.a1.a1', '300.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [4233, -1, 8570, -1, 3219, -1, 4996, -1], 'generators': [5132529041, 63497275003, 91767587507, 146494333804, 109882823127, 122109387504], 'label': '7200.c.75.a1.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.a1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.a1.b1', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 68225755
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['25.a1.a1'], 'contains': ['225.a1.a1', '300.b1.a2', '300.f1.a1', '300.f1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3225, -1, 6345, -1, 1944, -1, 8214, -1], 'generators': [5618498947, 63497275003, 91767587507, 146494333804, 109882823127, 122109387504], 'label': '7200.c.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': '3600.a', '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': '144.184'}
  • id: 68225756
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['25.a1.a1'], 'contains': ['225.a1.a1', '300.b1.a1', '300.f1.a1', '300.f1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3225, -1, 6543, -1, 1944, -1, 8445, -1], 'generators': [4645543588, 63497275003, 91767587507, 146494333804, 109882823127, 122109387504], 'label': '7200.c.75.b1.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.b1.a2', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.b1.a2', 'subgroup_fusion': None, 'weyl_group': '144.184'}
  • id: 68225757
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '30.a1.b1'], 'contains': ['180.a1.a1', '180.b1.a1', '180.c1.a1', '450.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7530, -1, 3970, -1, 5815, -1, 4510, -1], 'generators': [6791032020, 6162126234, 62276962503, 61054853203, 122109387504], 'label': '7200.c.90.a1.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': '90.a1.a1', 'projective_image': '3600.a', '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: 68225758
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '30.a1.a1'], 'contains': ['180.a1.b1', '180.b1.b1', '180.c1.b1', '450.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7530, -1, 7466, -1, 5815, -1, 2242, -1], 'generators': [2197763151, 91767587507, 91582193827, 109882823127, 122109387504], 'label': '7200.c.90.a1.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': '90.a1.b1', 'projective_image': '3600.a', '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: 68225759
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '10.a1.b1'], 'contains': ['200.a1.a1', '200.b1.a1', '200.b1.b1', '300.a1.a1', '300.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1642, -1, 9188, -1, 4585, -1, 7456, -1], 'generators': [73330086274, 97675793127, 151743167406, 31749856304, 122109387504], 'label': '7200.c.100.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '3600.a', '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': '36.10'}
  • id: 68225760
    {'ambient': '7200.c', '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': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.a1', '30.a1.a1', '30.b1.a1', '36.a1.a1', '60.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6060, -1, 6888, -1, 6055, -1, 2391, -1], 'generators': [35410550001, 65937900003, 34419153146, 25375393147, 122109387504], 'label': '7200.c.6.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
  • id: 68225761
    {'ambient': '7200.c', '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': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '25.a1.a1', '50.a1.a1'], 'contains': ['300.d1.a1', '300.e1.b1', '300.f1.a1', '400.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [2778, -1, 8111, -1, 2976, -1, 7788, -1], 'generators': [49033514824, 4645543588, 63497275003, 116093760018, 122109387504], 'label': '7200.c.100.b1.a1', '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.b1.a1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225762
    {'ambient': '7200.c', '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': '1200.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '25.a1.a1', '50.a1.b1'], 'contains': ['300.d1.b1', '300.e1.a1', '300.f1.b1', '400.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [2778, -1, 9874, -1, 2976, -1, 7046, -1], 'generators': [24501953774, 4645543588, 91767587507, 109882823127, 122109387504], 'label': '7200.c.100.b1.b1', '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.b1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 68225763
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.b1.a2', '360.a1.b1', '600.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6097, -1, 3203, -1, 8475, -1, 73, -1], 'generators': [35410550001, 52774623751, 54671098133, 122109387504], 'label': '7200.c.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '120.a1.a1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 68225764
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.b1'], 'contains': ['240.a1.b1', '240.b1.b1', '240.b1.b2', '360.a1.a1', '600.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6097, -1, 5497, -1, 8475, -1, 8140, -1], 'generators': [85498053770, 151683107297, 18951236390, 122109387504], 'label': '7200.c.120.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '120.a1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.b1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 68225765
    {'ambient': '7200.c', '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': '720.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '60.b1.a1'], 'contains': ['240.a1.a1', '360.c1.b1', '600.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7097, -1, 6219, -1, 7997, -1, 337, -1], 'generators': [35410550001, 119405088127, 54671098133, 122109387504], 'label': '7200.c.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '120.b1.a1', 'projective_image': '3600.a', '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': '12.4'}
  • id: 68225766
    {'ambient': '7200.c', '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': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '60.b1.b1'], 'contains': ['240.a1.b1', '360.c1.a1', '600.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7097, -1, 4869, -1, 7997, -1, 6768, -1], 'generators': [85498053770, 151683107297, 76579792069, 122109387504], 'label': '7200.c.120.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '120.b1.b1', 'projective_image': '3600.a', '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': '12.4'}
  • id: 68225767
    {'ambient': '7200.c', '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': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '30.a1.a1', '60.b1.a1'], 'contains': ['240.a1.a1', '360.d1.a1', '600.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5639, -1, 4307, -1, 6717, -1, 681, -1], 'generators': [5617926781, 116093760018, 91582193827, 122109387504], 'label': '7200.c.120.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '120.c1.a1', 'projective_image': '3600.a', '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': '20.4'}
  • id: 68225768
    {'ambient': '7200.c', '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': '1200.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '30.a1.b1', '60.b1.b1'], 'contains': ['240.a1.b1', '360.d1.b1', '600.c1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5639, -1, 5925, -1, 6717, -1, 7112, -1], 'generators': [63497584402, 12324220642, 24462891270, 122109387504], 'label': '7200.c.120.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '120.c1.b1', 'projective_image': '3600.a', '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': '20.4'}
  • id: 68225769
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1'], 'contains': ['600.e1.a1', '720.d1.a1', '1200.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [629, -1, 48, -1, 608, -1, 9944, -1], 'generators': [85625011892, 19446500575], 'label': '7200.c.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.a1', 'old_label': '120.d1.a1', 'projective_image': '7200.c', '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': '60.5'}
  • id: 68225770
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.b1'], 'contains': ['600.e1.a2', '720.d1.b1', '1200.d1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [629, -1, 246, -1, 608, -1, 9796, -1], 'generators': [2448281700, 19203562850], 'label': '7200.c.120.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.c1.b1', 'old_label': '120.d1.b1', 'projective_image': '7200.c', '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': '60.5'}
  • id: 68225771
    {'ambient': '7200.c', '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': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.b1', '30.a1.b1', '30.b1.b1', '36.a1.a1', '60.b1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6060, -1, 5340, -1, 6055, -1, 5703, -1], 'generators': [32970078200, 85498053770, 24609377520, 140439466896, 122109387504], 'label': '7200.c.6.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '6.a1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
  • id: 68225772
    {'ambient': '7200.c', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.b1.b1'], 'contains': ['288.a1.a1', '720.a1.a1', '720.a1.b1', '720.b1.a1', '720.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9903, -1, 2162, -1, 8187, -1, 2380, -1], 'generators': [35410550001, 122158215649, 122109387504], 'label': '7200.c.144.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225773
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1'], 'contains': ['288.a1.a1', '720.c1.a1', '720.c1.b1', '720.d1.a1', '720.d1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9082, -1, 840, -1, 8666, -1, 2833, -1], 'generators': [34274621881, 35410550001, 30722659381], 'label': '7200.c.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '7200.c', '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': '100.13'}
  • id: 68225774
    {'ambient': '7200.c', 'aut_centralizer_order': None, 'aut_label': '144.b2', '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': ['72.a1.a1'], 'contains': ['288.a1.a1', '720.c1.a1', '720.c1.b1', '720.d2.a1', '720.d2.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9446, -1, 1183, -1, 9010, -1, 2644, -1], 'generators': [35410550001, 30722659381, 124721487524], 'label': '7200.c.144.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.b2.a1', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b2.a1', 'subgroup_fusion': None, 'weyl_group': '100.13'}
  • id: 68225775
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '50.a1.b1', '75.a1.a1'], 'contains': ['300.e1.a1', '450.a1.a1', '600.c1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4426, -1, 7428, -1, 4155, -1, 3198, -1], 'generators': [24501953774, 63497275003, 91767587507, 109882823127, 122109387504], 'label': '7200.c.150.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.a1.a1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225776
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.b1', '30.b1.b1', '50.a1.a1', '75.a1.b1'], 'contains': ['300.e1.b1', '450.a1.b1', '600.c1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4426, -1, 8451, -1, 4155, -1, 5149, -1], 'generators': [63497275003, 4151760677, 146494333804, 109882823127, 122109387504], 'label': '7200.c.150.a1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.b1', 'old_label': '150.a1.b1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225777
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '50.a1.a1'], 'contains': ['300.a1.a1', '300.c1.a1', '300.d1.a1', '450.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [5002, -1, 6686, -1, 3578, -1, 4249, -1], 'generators': [34219934376, 149852740016, 62276962503, 61054853203, 122109387504], 'label': '7200.c.150.b1.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.b1.a1', 'projective_image': '3600.a', '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: 68225778
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.b1', '50.a1.b1'], 'contains': ['300.a1.b1', '300.c1.b1', '300.d1.b1', '450.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [5002, -1, 9068, -1, 3578, -1, 5386, -1], 'generators': [91767587507, 109882823127, 125772346976, 149668856901, 122109387504], 'label': '7200.c.150.b1.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.b1.b1', 'projective_image': '3600.a', '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: 68225779
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '36.a1.a1', '60.b1.b1', '90.a1.a1'], 'contains': ['360.a1.a1', '360.c1.a1', '360.d1.b1', '900.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7233, -1, 3766, -1, 7286, -1, 3732, -1], 'generators': [12324220642, 18654298760, 62276962503, 122109387504], 'label': '7200.c.180.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '3600.a', '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': '20.4'}
  • id: 68225780
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.b1', '36.a1.a1', '60.b1.a1', '90.a1.b1'], 'contains': ['360.a1.b1', '360.c1.b1', '360.d1.a1', '900.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7233, -1, 4575, -1, 7286, -1, 994, -1], 'generators': [2197763151, 91582193827, 109882823127, 122109387504], 'label': '7200.c.180.a1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.b1', 'old_label': '180.a1.b1', 'projective_image': '3600.a', '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': '20.4'}
  • id: 68225781
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1'], 'contains': ['360.a1.a1', '360.c1.a1', '900.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7777, -1, 3291, -1, 6238, -1, 5345, -1], 'generators': [6791032020, 12324220642, 62276962503, 122109387504], 'label': '7200.c.180.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': '180.b1.a1', 'projective_image': '3600.a', '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': '40.13'}
  • id: 68225782
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.a1.a1', '30.b1.b1', '50.a1.a1', '60.b1.a1', '100.a1.a1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [2753, -1, 8745, -1, 4719, -1, 6237, -1], 'generators': [73330086274, 97675793127, 41918946174, 97842054041, 122109387504], 'label': '7200.c.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': '3600.a', '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': '360.121'}
  • id: 68225783
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.b1'], 'contains': ['360.a1.b1', '360.c1.b1', '900.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7777, -1, 6304, -1, 6238, -1, 1227, -1], 'generators': [30703450491, 2197763151, 109882823127, 122109387504], 'label': '7200.c.180.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': '180.b1.b1', 'projective_image': '3600.a', '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': '40.13'}
  • id: 68225784
    {'ambient': '7200.c', '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': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.b1', '90.a1.a1'], 'contains': ['360.c1.a1', '900.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8727, -1, 4009, -1, 5815, -1, 4488, -1], 'generators': [6162126234, 62276962503, 61054853203, 122109387504], 'label': '7200.c.180.c1.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': '180.c1.a1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225785
    {'ambient': '7200.c', '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': '720.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.a1', '90.a1.b1'], 'contains': ['360.c1.b1', '900.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8727, -1, 7714, -1, 5815, -1, 1804, -1], 'generators': [2197763151, 91767587507, 109882823127, 122109387504], 'label': '7200.c.180.c1.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': '180.c1.b1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225786
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.a1.a1'], 'contains': ['400.a1.a1', '400.b1.a1', '400.b1.a2', '600.a1.a1', '600.a1.b1', '600.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [936, -1, 4937, -1, 1659, -1, 8659, -1], 'generators': [73330086274, 102315991353, 151743167406, 122109387504], 'label': '7200.c.200.a1.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': '200.a1.a1', 'projective_image': '3600.a', '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': '36.10'}
  • id: 68225787
    {'ambient': '7200.c', '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': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '50.a1.b1', '100.a1.a1'], 'contains': ['400.a1.a1', '600.c1.a1', '600.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1938, -1, 9459, -1, 4132, -1, 7876, -1], 'generators': [52944489281, 116093760018, 125772346976, 122109387504], 'label': '7200.c.200.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '200.b1.a1', 'projective_image': '3600.a', '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': '12.4'}
  • id: 68225788
    {'ambient': '7200.c', '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': '1200.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.b1', '50.a1.a1', '100.a1.a1'], 'contains': ['400.a1.a1', '600.c1.b1', '600.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1938, -1, 9952, -1, 4132, -1, 7456, -1], 'generators': [91572275002, 150823151748, 65938137554, 122109387504], 'label': '7200.c.200.b1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '200.b1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 68225789
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.a1.a1', '75.a1.b1', '75.b1.a1', '75.b1.a2'], 'contains': ['450.a1.a1', '450.a1.b1', '450.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3390, -1, 6862, -1, 2228, -1, 4912, -1], 'generators': [63497275003, 91767587507, 146494333804, 109882823127, 122109387504], 'label': '7200.c.225.a1.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.a1.a1', 'projective_image': '3600.a', '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': '144.184'}
  • id: 68225790
    {'ambient': '7200.c', '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': '240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.a1', '120.a1.a1', '120.b1.a1', '120.c1.a1'], 'contains': ['480.a1.a1', '720.a1.b1', '1200.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6510, -1, 4155, -1, 6717, -1, 681, -1], 'generators': [5617926781, 116093760018, 122109387504], 'label': '7200.c.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '240.a1.a1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225791
    {'ambient': '7200.c', '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': '240.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.d1.b1', '120.a1.b1', '120.b1.b1', '120.c1.b1'], 'contains': ['480.a1.b1', '720.a1.a1', '1200.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [6510, -1, 5183, -1, 6717, -1, 6560, -1], 'generators': [63497584402, 12324220642, 122109387504], 'label': '7200.c.240.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '240.a1.b1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225792
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1'], 'contains': ['480.a1.a1', '720.c1.b1', '1200.c1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5874, -1, 3193, -1, 7383, -1, 1381, -1], 'generators': [35410550001, 52774623751, 54671098133], 'label': '7200.c.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '240.b1.a1', 'projective_image': '7200.c', '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': '60.8'}
  • id: 68225793
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.a1.b1', '30.b1.a1', '50.a1.b1', '60.b1.b1', '100.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2753, -1, 9168, -1, 4719, -1, 6877, -1], 'generators': [49052738758, 61162115643, 123331803202, 125772346976, 122109387504], 'label': '7200.c.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': '3600.a', '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': '360.121'}
  • id: 68225794
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1'], 'contains': ['480.a1.a1', '720.c1.b1', '1200.c1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5874, -1, 3032, -1, 7383, -1, 1565, -1], 'generators': [35410550001, 137705863754, 54671098133], 'label': '7200.c.240.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '240.b1.a2', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 68225795
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.b1'], 'contains': ['480.a1.b1', '720.c1.a1', '1200.c1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5874, -1, 5340, -1, 7383, -1, 7512, -1], 'generators': [13041033010, 85498053770, 39051755983], 'label': '7200.c.240.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '240.b1.b1', 'projective_image': '7200.c', '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': '60.8'}
  • id: 68225796
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.b1'], 'contains': ['480.a1.b1', '720.c1.a1', '1200.c1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [5874, -1, 4648, -1, 7383, -1, 7328, -1], 'generators': [85498053770, 39051755983, 18951236390], 'label': '7200.c.240.b1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.b1', 'old_label': '240.b1.b2', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.b2', 'subgroup_fusion': None, 'weyl_group': '60.8'}
  • id: 68225797
    {'ambient': '7200.c', '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': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.b2.a1'], 'contains': ['1440.a1.a1', '1440.a1.b1', '1440.b1.a1', '1440.b1.b1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9722, -1, 911, -1, 8187, -1, 2747, -1], 'generators': [35410550001, 30722659381], 'label': '7200.c.288.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '7200.c', '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': '4.2'}
  • id: 68225798
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '60.b1.a1', '100.a1.a1', '150.b1.a1'], 'contains': ['600.a1.a1', '600.c1.a1', '600.d1.a1', '900.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4552, -1, 7392, -1, 5019, -1, 3260, -1], 'generators': [34219934376, 149852740016, 62276962503, 122109387504], 'label': '7200.c.300.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '300.a1.a1', 'projective_image': '3600.a', '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': '12.4'}
  • id: 68225799
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.b1', '60.b1.b1', '100.a1.a1', '150.b1.b1'], 'contains': ['600.a1.b1', '600.c1.b1', '600.d1.b1', '900.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [4552, -1, 8681, -1, 5019, -1, 6379, -1], 'generators': [109882823127, 125772346976, 149668856901, 122109387504], 'label': '7200.c.300.a1.b1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.b1', 'old_label': '300.a1.b1', 'projective_image': '3600.a', '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': '12.4'}
  • id: 68225800
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '75.b1.a2'], 'contains': ['600.e1.a1', '900.c1.a1', '1200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [1255, -1, 2146, -1, 219, -1, 9425, -1], 'generators': [4645543588, 38857825626, 110078508623, 122109387504], 'label': '7200.c.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': '3600.a', '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': '12.3'}
  • id: 68225801
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.b1', '75.b1.a1'], 'contains': ['600.e1.a2', '900.c1.a2', '1200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 300, 'diagramx': [1255, -1, 1907, -1, 219, -1, 9147, -1], 'generators': [122177894314, 5618498947, 38857825626, 122109387504], 'label': '7200.c.300.b1.a2', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '300.b1.a2', 'old_label': '300.b1.a2', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.a2', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 68225802
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.b1.a1'], 'contains': ['600.a1.a1', '600.c1.a1', '900.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [5124, -1, 4711, -1, 3511, -1, 5161, -1], 'generators': [149852740016, 62276962503, 62285712552, 122109387504], 'label': '7200.c.300.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.a1', 'old_label': '300.c1.a1', 'projective_image': '3600.a', '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': '24.14'}
  • id: 68225803
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.b1.b1'], 'contains': ['600.a1.b1', '600.c1.b1', '900.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [5124, -1, 7994, -1, 3511, -1, 5890, -1], 'generators': [66001806457, 109882823127, 149668856901, 122109387504], 'label': '7200.c.300.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.b1.b1', 'old_label': '300.c1.b1', 'projective_image': '3600.a', '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': '24.14'}
  • id: 68225804
    {'ambient': '7200.c', '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': '720.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['60.a1.a1', '60.d1.a1', '72.b1.b1', '120.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6650, -1, 7086, -1, 6754, -1, 1804, -1], 'generators': [35410550001, 94117978142, 12839455019, 122109387504], 'label': '7200.c.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '3600.a', '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': '120.35'}
  • id: 68225805
    {'ambient': '7200.c', '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': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.a1.a1', '100.b1.a1', '150.b1.a1'], 'contains': ['600.c1.a1', '900.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3926, -1, 7152, -1, 2740, -1, 4014, -1], 'generators': [49033514824, 63497275003, 116093760018, 122109387504], 'label': '7200.c.300.d1.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': '300.d1.a1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225806
    {'ambient': '7200.c', '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': '1200.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.a1.b1', '100.b1.b1', '150.b1.b1'], 'contains': ['600.c1.b1', '900.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3926, -1, 9343, -1, 2740, -1, 4770, -1], 'generators': [5132529041, 91767587507, 109882823127, 122109387504], 'label': '7200.c.300.d1.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': '300.d1.b1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225807
    {'ambient': '7200.c', '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': '60.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '60.d1.a1', '100.b1.b1', '150.a1.a1'], 'contains': ['900.d1.b1', '1200.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3525, -1, 8944, -1, 4603, -1, 2953, -1], 'generators': [24501953774, 91767587507, 109882823127, 122109387504], 'label': '7200.c.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': '3600.a', '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': '12.3'}
  • id: 68225808
    {'ambient': '7200.c', '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': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.b1', '60.d1.b1', '100.b1.a1', '150.a1.b1'], 'contains': ['900.d1.a1', '1200.a1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3525, -1, 8418, -1, 4603, -1, 6072, -1], 'generators': [91582350027, 1222581276, 63497275003, 122109387504], 'label': '7200.c.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': '3600.a', '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': '12.3'}
  • id: 68225809
    {'ambient': '7200.c', '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': '1200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.b1.a1', '75.b1.a2', '100.b1.a1'], 'contains': ['900.d1.a1', '1200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [2367, -1, 4354, -1, 1046, -1, 8918, -1], 'generators': [91582350027, 4645543588, 63497275003, 122109387504], 'label': '7200.c.300.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': '300.f1.a1', 'projective_image': '3600.a', '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': '12.3'}
  • id: 68225810
    {'ambient': '7200.c', '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': '1200.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.b1.a1', '75.b1.a2', '100.b1.b1'], 'contains': ['900.d1.b1', '1200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [2367, -1, 6551, -1, 1046, -1, 8399, -1], 'generators': [4645543588, 91767587507, 109882823127, 122109387504], 'label': '7200.c.300.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.b1.b1', 'old_label': '300.f1.b1', 'projective_image': '3600.a', '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': '12.3'}
  • id: 68225811
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.a1.b1', '180.a1.a1', '180.b1.a1'], 'contains': ['720.a1.a1', '720.c1.a1', '1800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7719, -1, 2635, -1, 7050, -1, 4935, -1], 'generators': [6791032020, 12324220642, 122109387504], 'label': '7200.c.360.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': '360.a1.a1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 68225812
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.a1.a1', '180.a1.b1', '180.b1.b1'], 'contains': ['720.a1.b1', '720.c1.b1', '1800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7719, -1, 2942, -1, 7050, -1, 1748, -1], 'generators': [146494240029, 2442743828, 122109387504], 'label': '7200.c.360.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': '360.a1.b1', 'projective_image': '3600.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1.b1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 68225813
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '72.a1.a1'], 'contains': ['720.b1.a1', '720.d1.a1', '720.d2.a1', '1800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6615, -1, 553, -1, 7716, -1, 3204, -1], 'generators': [34274621881, 124606653149, 122109387504], 'label': '7200.c.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '360.b1.a1', 'projective_image': '3600.a', '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': '10.1'}
  • id: 68225814
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.b1', '72.a1.a1'], 'contains': ['720.b1.b1', '720.d1.b1', '720.d2.b1', '1800.a1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6615, -1, 1568, -1, 7716, -1, 3021, -1], 'generators': [123388293774, 34274621881, 122109387504], 'label': '7200.c.360.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.b1', 'old_label': '360.b1.b1', 'projective_image': '3600.a', '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': '10.1'}
  • id: 68225815
    {'ambient': '7200.c', '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': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1'], 'contains': ['60.a1.b1', '60.d1.b1', '72.b1.a1', '120.b1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6650, -1, 5125, -1, 6754, -1, 5573, -1], 'generators': [32970078200, 85498053770, 36845716272, 122109387504], 'label': '7200.c.12.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '12.a1.b1', 'projective_image': '3600.a', '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': '120.35'}
  • id: 68225816
    {'ambient': '7200.c', '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': '360.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '120.b1.b1', '180.a1.a1', '180.b1.a1', '180.c1.a1'], 'contains': ['720.a1.a1', '1800.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8627, -1, 3522, -1, 6388, -1, 4751, -1], 'generators': [12324220642, 62276962503, 122109387504], 'label': '7200.c.360.c1.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': '360.c1.a1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225817
    {'ambient': '7200.c', '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': '360.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.b1', '120.b1.a1', '180.a1.b1', '180.b1.b1', '180.c1.b1'], 'contains': ['720.a1.b1', '1800.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8627, -1, 6242, -1, 6388, -1, 1931, -1], 'generators': [2197763151, 109882823127, 122109387504], 'label': '7200.c.360.c1.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': '360.c1.b1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225818
    {'ambient': '7200.c', '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': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.b1', '72.b1.a1', '120.c1.a1', '180.a1.b1'], 'contains': ['720.a1.b1', '1800.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7076, -1, 3904, -1, 6051, -1, 2117, -1], 'generators': [91582193827, 2442743828, 122109387504], 'label': '7200.c.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '360.d1.a1', 'projective_image': '3600.a', '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': '10.1'}
  • id: 68225819
    {'ambient': '7200.c', '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': '60.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '72.b1.b1', '120.c1.b1', '180.a1.a1'], 'contains': ['720.a1.a1', '1800.b1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7076, -1, 6016, -1, 6051, -1, 3660, -1], 'generators': [12324220642, 24462891270, 122109387504], 'label': '7200.c.360.d1.b1', 'mobius_quo': None, 'mobius_sub': 60, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '360.d1.b1', 'projective_image': '3600.a', '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': '10.1'}
  • id: 68225820
    {'ambient': '7200.c', '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': '400.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['100.b1.a1', '100.b1.b1', '200.a1.a1', '200.b1.a1', '200.b1.b1'], 'contains': ['800.a1.a1', '1200.a1.a1', '1200.a1.b1', '1200.b1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1709, -1, 9494, -1, 1947, -1, 6939, -1], 'generators': [4645543588, 116093760018, 122109387504], 'label': '7200.c.400.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '400.a1.a1', 'projective_image': '3600.a', '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': '4.2'}
  • id: 68225821
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['200.a1.a1'], 'contains': ['800.a1.a1', '1200.c1.a1', '1200.c1.b1', '1200.d1.a2'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [601, -1, 5151, -1, 2374, -1, 7868, -1], 'generators': [110068370006, 88164965027, 151743167406], 'label': '7200.c.400.b1.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': '400.b1.a1', 'projective_image': '7200.c', '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': '36.10'}
  • id: 68225822
    {'ambient': '7200.c', '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': '3600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['200.a1.a1'], 'contains': ['800.a1.a1', '1200.c1.a1', '1200.c1.b1', '1200.d1.a1'], 'core': '7200.a1.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [601, -1, 4990, -1, 2374, -1, 8055, -1], 'generators': [110068370006, 102315991353, 151743167406], 'label': '7200.c.400.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '100.a1.a1', 'old_label': '400.b1.a2', 'projective_image': '7200.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.b1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 68225823
    {'ambient': '7200.c', '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': '1800.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.b1', '150.a1.a1', '150.b1.b1', '225.a1.a1'], 'contains': ['900.a1.a1', '900.b1.b1', '900.d1.b1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5588, -1, 7549, -1, 3171, -1, 3495, -1], 'generators': [63497275003, 91767587507, 109882823127, 122109387504], 'label': '7200.c.450.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': '450.a1.a1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225824
    {'ambient': '7200.c', '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': '1800.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '150.a1.b1', '150.b1.a1', '225.a1.a1'], 'contains': ['900.a1.a1', '900.b1.a1', '900.d1.a1'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5588, -1, 6562, -1, 3171, -1, 4251, -1], 'generators': [63497275003, 146494333804, 109882823127, 122109387504], 'label': '7200.c.450.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.b1', 'old_label': '450.a1.b1', 'projective_image': '3600.a', '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': '24.13'}
  • id: 68225825
    {'ambient': '7200.c', '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': '1800.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.a1.a1'], 'contains': ['900.a1.a1', '900.b1.a1', '900.b1.b1', '900.c1.a1', '900.c1.a2'], 'core': '3600.a1.a1', 'coset_action_label': None, 'count': 225, 'diagramx': [3014, -1, 4842, -1, 2228, -1, 5577, -1], 'generators': [31930090641, 146494333804, 109882823127, 122109387504], 'label': '7200.c.450.b1.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': '450.b1.a1', 'projective_image': '3600.a', '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': '8.5'}